Non-Cooperative Game Theory

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Airport profit games are a generalization of airport cost games as well as of bankruptcy games. In this paper we present a simple algorithm to compute the nucleolus of airport profit games. In addition we prove that there exists an unique consistent allocation rule in airport profit problems, and it coincides with the nucleolus of the associated TU game. * We acknowledge the advice from Peter Sudhölter in shortening some proofs. This work has been financed by project 1/UPV 00031.321-HA-7903/2000 and DGES Ministerio de Educación y Ciencia (project BEC2000-0875).

In this paper, a utility-based joint power and rate adaptive algorithm (UPRA) is proposed to alleviate the influence of channel variation by using softened signal-to-interference-andnoise ratio (SINR) requirements. The transmission power and rate of each user will be adjusted to maximize its own net-utility according to the states of channel, which results in a balance between the effective transmission rate and power consumption. Although the UPRA works based on a non-cooperative game, cooperation among users can be achieved so that the throughput of the whole network will be improved. The convergence of the algorithm has also been studied in both feasible and infeasible cases. Index Terms-Joint power and rate adaptive, non-cooperative game, effective transmission rate, wireless ad hoc networks. T RANSMISSION power and rate have significant impacts on the performance of wireless networks. On one hand, high transmission rate requires high Signal-to-Interferenceand-Noise Ratio (SINR). On the other hand, high transmission power means more energy consumption and interference to other users. Although the issue of joint power and rate control is challenging, it offers more flexibility in radio resource management thus the possibility of better network performance. Non-cooperative game model was employed for power control in wireless networks in previous work. One characteristic of non-cooperative games is "all players for themselves" . Each node tries to maximize its own net-utility, which is defined as utility minus cost. With distinct optimizing objectives, different utility functions were formulated in prior work, such as throughput per unit power consumption [2], frame outage [3], Shannon capacity [4] and sigmoid-like softened SINR requirement . The cost was often modeled as a linear function of transmission power. In this way, cooperation was introduced to the non-cooperative game. It should be pointed out that all the above algorithms were designed for cellular networks where power control schemes can be implemented at base stations. However, power control in wireless ad hoc networks can only work based on local measurements. In [6], a joint transmission power and rate control algorithm based on game theory, called Distributed Power and Rate Control based on Step-up Pricing Game (DPRC/SPG), was proposed for wireless ad hoc networks. Its net-utility function is defined as the normalized transmission rate minus the cost of Paper approved by S. A. Jafar, the Editor for Wireless Communication Theory and CDMA of the IEEE Communications Society. Manuscript

In this paper we study a two stage contest where the strength of players in the second stage depends on the result of the contest in the first stage. We show that this contest displays properties that are not present in one shot contests. Non-symmetric players make different efforts in the first stage and rent dissipation in the first period may be large. We study the conditions under which the discouragement effect holds. In addition, new issues emerge like the evolution of the strengths and the shares of the prize during the game.

We introduce a new representation scheme for coalitional games, called coalition-flow networks (CF-NETs), where the formation of effective coalitions in a task-based setting is reduced to the problem of directing flow through a network. We show that our representation is intuitive, fully expressive, and captures certain patterns in a significantly more concise manner compared to the conventional approach. Furthermore, our representation has the flexibility to express various classes of games, such as characteristic function games, coalitional games with overlapping coalitions, and coalitional games with agent types. As such, to the best of our knowledge, CF-NETs is the first representation that allows for switching conveniently and efficiently between overlapping/nonoverlapping coalitions, with/without agent types. We demonstrate the efficiency of our scheme on the coalition structure generation problem, where near-optimal solutions for large instances can be found in a matter of seconds. tween co-existing coalitions) .

A bs t ract. On the basis of experime nt , two groups arr ived ind ep endently at similar conjectures on the na t ure of optimal st rategies employed in large random ga mes . The first conject ur e was mad e by Kuhn a nd Qu andt in 1963; the second was mad e by the present authors in 1987. In tradition al m athematics such duplication is supe rfluous . In expe rimental mathem atics it may pr ovid e mu tua l confirmation .

Game theory, the mathematical study of strategic interactions among rational decision-makers, has emerged as a powerful analytical framework within operations research. This thesis explores the use of game theory to model and solve real-world operational problems involving conflict, competition, and cooperation. Applications include cost-sharing in logistics, competitive bidding in transport contracts, and coordination in decentralized supply chains. By combining theoretical analysis with simulation-based experimentation, this study demonstrates how strategic models can lead to more efficient, stable, and fair outcomes in operational settings. Emphasis is placed on both cooperative and non-cooperative frameworks, Nash equilibria, and repeated interactions. The thesis concludes with actionable insights for policy-makers, operational managers, and researchers interested in strategic decision-making under uncertainty.

One of the key challenges in Internet of Things (IoT) networks is to connect many different types of autonomous devices while reducing their individual power consumption. This problem is exacerbated by two main factors: a) the fact that these devices operate in and give rise to a highly dynamic and unpredictable environment where existing solutions (e.g., water-filling algorithms) are no longer relevant; and b) the lack of sufficient information at the device end. To address these issues, we propose a regret-based formulation that accounts for arbitrary network dynamics: this allows us to derive an online power control scheme which is provably capable of adapting to such changes, while relying solely on strictly causal feedback. In so doing, we identify an important tradeoff between the amount of feedback available at the transmitter side and the resulting system performance: if the device has access to unbiased gradient observations, the algorithm's regret after T stages is O(T -1/2 ) (up to logarithmic factors); on the other hand, if the device only has access to scalar, utilitybased information, this decay rate drops to O(T -1/4 ). The above is validated by an extensive suite of numerical simulations in realistic channel conditions, which clearly exhibit the gains of the proposed online approach over traditional water-filling methods.

We explore how peace or war can occur in the presence of commitment problems. These problems can be reduced by institutions of good governance or, alternatively, state capacity which (a) can be considered a collective good and (b) can be improved through investments. We show how the likelihood of a peace agreement depends on the level of state capacity and on investments in state capacity made by adversaries. In accordance with existing evidence but contrary to various theories of conflict, we find that income levels unambiguously increase the chance of peace. Among other issues, we discuss the critical role of external actors in encouraging or discouraging commitment and in developing good governance institutions.

The Computational Grid (CG) provides a wide distributed platform for high end computing intensive applications. Scheduling on Computational grid is known to be NP-Hard problem and requires an efficient solution. Recently, quantum inspired computing has been introduced in the literature to solve such a complex combinatorial optimization problem efficiently. Combination of Genetic Algorithm (GA) and quantum concept evolves a new meta-heuristic technique known as Quantum Genetic Algorithms (QGA). QGA is a search procedure based on evolutionary computation and Quantum Computing (QC). This paper proposes a novel technique of scheduling in computational grid using QGA. The work simulates the model to study its performance. It also makes a comparative study with a GA-based scheduling model. Simulation results reveal the effectiveness of the model.

The recent literature on cost allocation lacks consensus on what is an appropriate de…nition of the consistency axiom. We take this as evidence that a careful reexamination is necessary. The starting point of our critique is the widely adopted de…nition proposed in , which we show to be conceptually ‡awed. Rectifying this ‡aw leads to a de…nition of consistency which already appeared in the recent literature though without satisfactory conceptual justi…cation. We o¤er a classi…cation of the existing de…nitions of the consistency axiom by relating them to the de…nitions of consistency in cooperative games suggested in and . We argue that only the latter leads to a meaningful interpretation of consistency when production externalities are present.

In this paper, we propose coordination procedures for a multi-echelon supply chain in which the appropriate profit-sharing rate is allocated for each supply chain member. The search process is first developed to maximise the total compromised profit of a two-member supply chain. From the achieved profit-sharing rate, the best ordering quantity is also determined. Then, a cascading procedure is also proposed for searching the best profit-sharing ratios for each member in the multi-echelon supply chain. Our proposed procedures are validated by comparing it with the fixed profit-sharing scheme. We have also investigated different scenarios to test the effect of demand variations on total cost at different profit-sharing rates. The obtained results are promising. [

Wide area research and education networks, such as ESnet and Internet2 in the US and GEANT in Europe, have recently deployed software that makes possible to reserve bandwidth in the form of dynamic circuits. Such circuits offer guaranteed QoS to specific data flows, significantly increasing the reliability and predictability of data transfers. In this paper, we study the problem of constructing routes and scheduling bandwidth reservations for data transfers between multiple pairs of end sites. We develop an algorithm, called RRM, to solve this problem. Our objective is to maximize the number of satisfied data transfer requests while minimizing the total data transfer times. We further prove that our problem is NP-hard and compare our algorithm with a baseline FCFS algorithm through simulations. The simulations indicate that our algorithm accommodates up to 160% more requests and achieves up to 50% shorter average data transfer times than the baseline algorithm.

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user's QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed noncooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a "size" for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users' delay profiles and the delay performance of the users at Nash equilibrium is quantified.

We consider repeated multi-player games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multi-agent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are "payoff based" processes, in which at any stage, players only know their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff based processes for increasingly general scenarios and prove that after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network.

The Hour-Al-Azim transboundary wetland, one of Iran's most significant wetlands, is facing desiccation due to a disregard for environmental flow. A significant portion of the wetland has dried up, leading to the emergence of dust storms with detrimental effects on the region. Therefore, the imperative lies in fully restoring the wetland to mitigate the damages caused by dust storms and drought. In this study, considering the agricultural land area in the Karkheh River Basin and estimating the water requirements of the agricultural sector, the allocation scenario that satisfies all stakeholders was determined using a cooperative game theory approach and Shapley value. The results indicated that complete wetland revival is not feasible considering the available water resources. Hence, solutions were proposed to reduce water consumption considering the virtual water trade approach and ecosystem services payment method. All potential options for the government and farmers toward complete wetland revival were identified using sequential game theory. Ultimately, the findings demonstrated that adopting a cooperative approach to reduce cultivated areas benefits both farmers by increasing profits and the government by simultaneously achieving the goal of wetland revival.

Task scheduling and resource allocation are the crucial issues in any large scale distributed system, such as Computational Grids (CGs). However, traditional computational models and resolution methods cannot effectively tackle the complex nature of Grid, where the resources and users belong to many administrative domains with their own access policies, users' privileges, etc. Recently, researchers are investigating the use of game theoretic approaches for modelling task and resource allocation problems in CGs. In this paper, we present a compact survey of the most relevant research proposals in the literature to use game-based models for the resource allocation problems and their resolution using metaheuristic methods. We emphasize the need of the translation of the traditional economical models into the game scenarios and the use of metaheuristic schedulers for solving such games in order to address the new complex scheduling and allocation criterions. We study the case of asymmetric Stackelberg game used for modelling the Grid users' behavior, where the security and reliability criterions are aggregated and defined as the users' costs functions. The obtained results show the efficiency of the hybridization of heuristic-based approaches with game models, which enables to include additional requirements and features into the computational models and tackle more effectively the resolution of the applied schedulers.

The study aims to create an integrated framework of analysis allowing the optimization of government decisions to intervene in case of a major terrorist attack for limiting the consequences and restoring order and functionality, based on a set of specific models. This initiative is due to the lack of knowledge in this area of research and it is justified by the existence of new risks, as the risk of terrorism. Internationally there is a growing trend in conducting researches on the extreme risk events, which should lead to an intensification of scientific knowledge at national level.

A new noncooperative eigencoding algorithm is introduced for multiple-input multiple-output (MIMO) ad hoc networks. The algorithm performs generalized waterfilling with respect to its transmit covariance matrix and the receive node covariance matrix, both of which can be estimated locally. A cooperative algorithm is also developed as a benchmark in simulations. Simulation results show that the noncooperative algorithm performance is close to that of the cooperative method and is much better than greedy optimization. A game theoretic interpretation of the algorithm is also provided.

In this paper, we have proposed a new approach of routing and wavelength assignment algorithms, called Possible Available Wavelength (PAW) algorithm. The weight of a link is used as the main factor for routing decision in PAW algorithm. The weight of a link is defined as a function of hop count and available wavelengths. This function includes a determination factor of the number of wavelengths that are being used currently and are supposed to be available after a certain time. The session requests from users will be routed on the links that has the greatest number of link weight by using Dijkstra's shortest path algorithm. This means that the selected lightpath will has the least hop count and the greatest number of possible available wavelengths. The impact of proposed link weight computing function on the blocking probability and link utilization is investigated by means of computer simulation and comparing with the traditional mechanism. The results show that the proposed PAW algorithm can achieve the better performance in terms of the blocking probability and link utilization.

 Nishihara (1997) shows that not knowing the order of move may allow for rational  cooperation  We test this theory in an economic experiment  The experimental treatments vary transparency regarding subjects' order of move  Knowing the order of move does not result in less cooperation, and may even increase  cooperation

In this paper we study an expression for all additive, symmetric and efficient solutions, i.e., the set of axioms that traditionally are used to characterize the Shapley value except for the dummy axiom. Also, we obtain an expression for this kind of solutions by including the self duality axiom. These expressions allow us to give an alternative formula for the

Coase and Aumann-Myerson's solution for Network Formation Games: Misleading Policy Implications. Ricardo Nieva∗ RIT and University of Minnesota Email: rxngla@rit.edu Phone(585) 475-4647 Fax:(585) 475-2510 Website: http://www.rit.edu/~rxngla/ November 2002 ...

To avoid the single point of failure for the certificate authority (CA) in MANET, a decentralized solution is proposed where nodes are grouped into different clusters. Each cluster should contain at least two confident nodes. One is known as CA and the another as register authority RA. The Dynamic Demilitarized Zone (DDMZ) is proposed as a solution for protecting the CA node against potential attacks. It is formed from one or more RA node. The problems of such a model are: (1) Clusters with one confident node, CA, cannot be created and thus clusters' sizes are increased which negatively affect clusters' services and stability. (2) Clusters with high density of RA can cause channel collision at the CA. (3) Clusters' lifetime are reduced since RA monitors are always launched (i.e., resource consumption). In this paper, we propose a model based on mechanism design that will allow clusters with single trusted node (CA) to be created. Our mechanism will motivate nodes that do not belong to the confident community to participate by giving them incentives in the form of trust, which can be used for cluster's services. To achieve this goal, a RA selection algorithm is proposed that selects nodes based on a predefined selection criteria function and location (i.e., using directional antenna). Finally, empirical results are provided to support our solutions.

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

To represent an ethics of philosophical origin in computational form, thereby enabling agents to adhere to universal and unconditional ethical rules, we propose modifying the hedonic model by introducing ethical constraints based on rule generalization. This enhancement aims to enrich interactions within a heterogeneous multi-agent environment. We specifically explore integrating Immanuel Kant's ethical principles, particularly the categorical imperative, into a multi-agent hedonic game model. While traditionally centered on agents' personal preferences, this model can be refined by incorporating strict moral imperatives. The outcome of this approach is a formal representation of ethical principles, providing a framework for ethical decision-making in multi-agent systems.

Utility theories for the de¯nitions of cooperative games and associated solution concepts are discussed. A game with side payments needs the assumptions of transferable utility and side payments. We discuss the axioms for the transferable utility assumption and also the role of side payments for various solution concepts. We also discuss games without side payments, which do not require the assumptions of transferable utility and side payments. We see how some solution concepts depend upon these assumptions.

We develop a strategic model of network interdiction in a non-cooperative game of flow. An adversary, endowed with a bounded quantity of bads, chooses a flow specifying a plan for carrying bads through a network from a base to a target. Simultaneously, an agency chooses a blockage specifying a plan for blocking the transport of bads through arcs in the network. The bads carried to the target cause a target loss while the blocked arcs cause a network loss. The adversary earns and the agency loses from both target loss and network loss. The adversary incurs the expense of carrying bads. In this model we study Nash equilibria and find a power law relation between the probability and the extent of the target loss. Our model contributes to the literature of game theory by introducing non-cooperative behavior into a Kalai-Zemel (cooperative) game of flow. Our research also advances models and results on network interdiction.

On 20 and 21 January 2025, the GameTable COST Action's Working Group 1 convened in London for a meeting focused on game-playing artificial intelligence (AI), including search algorithms, knowledge representation, and reinforcement learning. The first day featured participant presentations, while the second day was dedicated to plenary and small group discussions. A significant outcome was the identified need for accessible resources to bridge AI and cultural heritage research. This report provides a summary of the discussions and talks that took place during the meeting.

We generalize exactness to games with non-transferable utility (NTU). In an exact game for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We study five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex

We show that the Shapley-Shubik power index on the domain of simple (voting) games can be uniquely characterized without the e¢ ciency axiom. In our axiomatization, the e¢ ciency is replaced by the following weaker requirement that we term the gain-loss axiom: any gain in power by a player implies a loss for someone else (the axiom does not specify the extent of the loss). The rest of our axioms are standard: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, and dummy.

We prove a representation theorem for the core of a non-atomic game of the form v = fOil, where Il is a finite dimensional vector of non-atomic measures and f is a non-decreasing continuous concave function on the range of Il. The theorem is stated in terms of the sub gradients of the function f. As a consequence of this theorem we show that the game v is balanced (i. e., has a non-empty core) iff the function f is homogeneous of degree one along the diagonal of the range of Il, and it is totally balanced (i.e., every subgame of v has a non-empty core) iff the function f is homogeneous of degree one in the entire range of Il. We also apply our results to some non-atomic games which occur in economic applications.

We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition: the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index. JEL Classification Numbers: C71, D72.

In this paper, we model socially-embedded games. We use non-cooperative game forms with pure strategy Nash equilibria and embed them through framing structures. These frames alter how players perceive the game, or rule out the choice of some elements of players' option sets. In this way, we explicitly link the notion of social game to concepts taken from Erving Goffman's theory of interaction. According to Goffman, game theory is flawed because it applies a single-level model to two-leveled situations, ignoring the fact that people form impressions and expectations during or before any strategic game. In this essay, we provide a set-up endowed with these two levels. Firstly, players endogenize a given setting and frame the interaction. This determines what kind of game they will play. Secondly, they select Nash equilibrium strategies. As we shall discuss, it is possible in this way to consider how frames operate and what role they have in determining Nash solutions of non-cooperative games.

In this paper, we model socially-embedded games. We use non-cooperative game forms with pure strategy Nash equilibria and embed them through framing structures. These frames alter how players perceive the game, or rule out the choice of some elements of players' option sets. In this way, we explicitly link the notion of social game to concepts taken from Erving Goffman's theory of interaction. According to Goffman, game theory is flawed because it applies a single-level model to two-leveled situations, ignoring the fact that people form impressions and expectations during or before any strategic game. In this essay, we provide a set-up endowed with these two levels. Firstly, players endogenize a given setting and frame the interaction. This determines what kind of game they will play. Secondly, they select Nash equilibrium strategies. As we shall discuss, it is possible in this way to consider how frames operate and what role they have in determining Nash solutions of non-cooperative games.

Summary. 'Coordination' as used here is understood in the following way: Agents solve problems in on-going dialogue under mutual control and according to stable, well-understood patterns. In task-oriented dialogue the social frame for coordination is fixed. The need for coordination among agents arises because of differences in information, the dominant dialogue pattern 'directive -reply', and because of incompatibilities with respect to speakers' ontologies, language variation and agents' focus management. We discuss three dialogue examples showing coordination in some detail. In all of them the coordination problem is solved via a side sequence. Side sequences can be implemented either as autonomous dialogue contributions or they can be fused into the utterances they start from. Grammars treating 'syntax-in-dialogue' and, above all, side sequences, have to meet several constraints: They must describe various forms of extraposition to the right and long distance dependencies, produce and analyse by increments, and shift from production to reception and vice versa. All these patterns will be of relevance for the man-machine-interaction focused upon in the research unit ,,Situated Artificial Communicators". It is suggested to set up the theory of grammar needed to accomplish all that within a theory of n-Person Cooperative Games. Zusammenfassung. Koordination im Dialog bedeutet, daß auftretende Probleme unter wechselseitiger Kontrolle der Agenten nach festgelegten Verfahren gelöst werden. In aufgabenorientierten Dialogen ist der soziale Rahmen für Koordination festgelegt. Koordination wird erforderlich wegen des Informationsgefälles zwischen Instrukteur und Konstrukteur, des dominanten Dialogmusters ,,Direktive geben" -,,Direktive befolgen" sowie der Unterschiede in den Bereichen Sprecherontologie, Sprachvariation und Fokussteuerung. Wir geben drei Dialogbeispiele für Koordination, bei denen das Koordinationsproblem über eine Nebensequenz gelöst wird. Nebensequenzen, sog. ,,Verständigungssequenzen", können als klar begrenzter, autonomer Subdialog realisiert oder in die Ausgangsäußerung eingefügt sein. Eine Syntax für den Dialog, insbesondere für Nebensequenzen und deren Einbettung, muß spezielle Konstruktionen wie Aus-klammerung und Nachtrag erfassen, inkrementell operieren und zwischen Produktion und Rezeption hin-und herschalten können. Über alle diese Fähigkeiten sollte ein Situierter Künstlicher Kommunikator verfügen. Es wird vorgeschlagen, das dazu benötigte Grammatikmodell im Rahmen einer Theorie der Kooperativen Mehr-Personen-Spiele zu konzipieren.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the semantics given by category theory. We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.

This paper explores a game-theoretic model for task allocation in distributed systems, where processors with varying speeds and external load factors are considered strategic players. The goal is to understand the impact of processors' strategic behaviors on workload management and overall system efficiency, focusing on the attainment of a pure strategy Nash Equilibrium (NE). The research rigorously develops a formal mathematical model and validates it through extensive simulations, highlighting how NE ensures stability but may not always yield optimal system performance. The adaptive algorithms for dynamic task allocation are proposed to enhance efficiency in real-time processing environments. Results demonstrate that while NE provides stability, the adoption of optimal cooperative strategies significantly improves operational efficiency and reduces transaction costs. The findings contribute valuable insights into the strategic interactions within computational frameworks, offering guidelines for developing more efficient systems. This study not only advances the theoretical understanding of strategic task allocation but also has practical implications for system design and policy-making in areas such as cloud computing and traffic management.

A new noncooperative eigencoding algorithm is introduced for multiple-input multiple-output (MIMO) ad hoc networks. The algorithm performs generalized waterfilling with respect to its transmit covariance matrix and the receive node covariance matrix, both of which can be estimated locally. A cooperative algorithm is also developed as a benchmark in simulations. Simulation results show that the noncooperative algorithm performance is close to that of the cooperative method and is much better than greedy optimization. A game theoretic interpretation of the algorithm is also provided.

We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as non-cooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of bestresponse policies in the non-cooperative case. We present an algorithm to compute equilibria policies in the case of two noncooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of the other mobile. Our results are illustrated and validated through various numerical examples.

The conventional definition of a cooperative game G(N,V ) with a set of players N = {1, . . . , n} and a characteristic function V, is quite rigid to alterations of the set of players N . Moreover, it may necessitate a large input of size that is exponential in n. However, the characteristic function of many games allows a simple, efficient and flexible presentation of the game. Here we deal with a set of games that we call regular games, which have a simple presentation: In regular games each player is characterized by a vector of quantitative properties, and the characteristic function value of a coalition depends only on the vectors of properties of its members. We show that some regular games in which players can cooperate with respect to some of their resources and whose immediate formulation does not fit the framework of market games, can nevertheless be transformed into the form of market games and hence they are totally balanced. In particular, they lead to a core allocation...

We propose a cooperative solution concept for games in extensive form that incorporates both cooperation and subgame perfection. This new concept, which we label the subgame-perfect core, is a refinement of the core of an extensive game in the same sense as the set of subgame-perfect Nash equilibria is a refinement of the set of Nash equilibria. Moreover, each subgame perfect core payoff vector can be obtained as a subgame-perfect Nash equilibrium payoff vector of a modified extensive game. We establish several additional properties of the subgame-perfect core and demonstrate its applicability by studying three applications: the centipede game, the two-player infinite bargaining game of alternating offers, and a dynamic game of climate change. In addition, we motivate and introduce a concept of subgame-perfect strong Nash equilibrium of an extensive game and show that it is coalition proof.

This paper brings together two of the most important solution concepts of game theorysubgame-perfect Nash equilibrium of a non-cooperative game and the core of a cooperative game. Our approach rests on two fundamental ideas: (1) Given an extensive game, the formation of a coalition leads to a new game where all the members of the coalition become one player. (2) At the origin of any subgame, the only possible coalitions consist of players who have decision nodes in the subgame. We introduce a concept of subgame perfect cooperative equilibrium, which we label the -core of an extensive game. We provide a necessary and sufficient condition for the existence of the -core of an extensive game of perfect information. As a motivating example, we formulate the problem of global warming as a dynamic game with simultaneous moves and show that if the payoff functions are quadratic, then the -core of the game is nonempty.