Tit for tat Strategy

his article dissects Donald Trump’s radical trade agenda—popularized as the Mar-a-Lago Accord—through the lens of strategic irrationality, game theory, and macroeconomic trade-offs. Far from erratic, Trump’s so-called Madman Strategy reveals a calculated framework blending currency devaluation, coercive debt restructuring, and security-linked trade incentives. Yet in seeking to reassert U.S. global dominance, this aggressive doctrine may trigger an unintended boomerang effect: accelerating European integration by exposing structural dependencies on American protection. As U.S. policy pivots from multilateralism to unilateral leverage, the risk of systemic backlash grows—potentially reshaping the geopolitical order. This paper argues that Trump’s effort to “Make America Great Again” could paradoxically catalyze the emergence of a more unified, autonomous Europe.

Keywords: Trump trade strategy, Mar-a-Lago Accord, Madman theory, European strategic autonomy, debt restructuring, dollar devaluation, game theory, U.S. foreign policy, geopolitical backlash, EU integration

This article delves into the strategic logic behind Donald Trump's unconventional political behavior, particularly his approach to trade policy and international negotiations. Trump's often unpredictable and seemingly irrational actions—ranging from abrupt policy reversals to controversial statements—are examined through the lens of the "Madman Theory," originally popularized by President Richard Nixon. This theory suggests that such erratic behavior may be a deliberate strategy designed to enhance one's negotiation power by exploiting the belief that irrational actions may lead adversaries to make concessions to avoid escalation. The paper explores the potential effectiveness and risks of this strategy in the context of Trump’s neo-mercantilist approach, which seeks to reduce trade deficits and restore American dominance, especially in light of global competition from China. It also discusses the potential dangers of a leader employing the Madman Strategy in a globalized world, where miscalculation could lead to catastrophic outcomes, such as nuclear conflict. Finally, the article proposes strategic responses for international actors, drawing on game theory and historical examples, including the concept of "generous tit for tat" and the benefits of de-escalating protectionist policies to foster global cooperation and peace.

This paper examines the inconsistency between Western nations’ proclaimed universal values and their selective application to non-Western actors like China. Using game theory, it explores the power dynamics and societal differences that create a cooperation dilemma, modeled as a modified prisoner’s dilemma. The analysis reveals that these tensions undermine effective responses to global challenges such as climate change and pandemics.

To address these issues, the paper proposes three strategies: selective cooperation on shared priorities, technological collaboration beyond political divides, and flexible global standards adaptable to regional contexts. These solutions aim to foster pragmatic dialogue and mutual respect, essential for overcoming ideological divides and enhancing global resilience. Ultimately, the study underscores that sustained cooperation is not optional but vital for addressing worldwide crises and creating a shared future.

Keywords: universal values, double standard, Western nations, China, game theory, global cooperation, geopolitical tensions, climate change, pandemics, selective cooperation, technological collaboration, flexible standards, prisoner’s dilemma, asymmetric power dynamics.

In evolutionary algorithms that evolve populations of strategies for the Iterated Prisoner's Dilemma, higher levels of cooperation evolve when the strategies engage in longer contests. When IPD-playing organisms are segregated into clans, with different strategies for contests with members of the same and other clans, populations evolve higher levels of cooperation for contests within clans. Cooperation between members of different clans increases with the length of their contests, but decreases when there are more clans. When organisms use the same strategy for contests with friends and with strangers, the difference between cooperation within and between clans is smaller, but persists.

In evolutionary algorithms that evolve populations of strategies for the Iterated Prisoner's Dilemma, higher levels of cooperation evolve when the strategies engage in longer contests. When IPD-playing organisms are segregated into clans, with different strategies for contests with members of the same and other clans, populations evolve higher levels of cooperation for contests within clans. Cooperation between members of different clans increases with the length of their contests, but decreases when there are more clans. When organisms use the same strategy for contests with friends and with strangers, the difference between cooperation within and between clans is smaller, but persists.

On 5–12 January, the 8th Congress of the ruling Workers’ Party of Korea was held. Decisions adopted during this meeting suggest the intent to tighten state control over the economy. North Korea will also develop its nuclear and missile programmes, treating them as elements of pressure on the U.S. and South Korea. The confrontational nature of the North Korean leadership’s decisions increases the risk of escalating tensions on the Korean Peninsula and further reduces the prospects of talks with the U.S. on denuclearisation.

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions

This paper deals with the morphogenesis of spatialized cooperative relations and with the role of proximity in the evolution, persistence and coexistence of various local strategies. The first part is devoted to a presentation of the analysis of cooperative relations in the evolutionary game theory. In the second part of the paper are presented various simulations on the emergence and evolution of localized cooperative relations, based on endogenous mutations and genetic algorithms. They reveal that a cooperative behavior is a stable, even if complex strategy, and that its emergence and diffusion are favored by the spatial character of inter firms relations. In addition, the results confirm that various strategies can locally coexist and be maintained, generally temporarily.

This article investigates the conditions under which cooperation will emerge in a world of egoists without central authority. This problem plays an important role in such diverse fields as political philosophy, international politics, and economic and social exchange. The problem is formalized as an iterated Prisoner's Dilemma with pairwise interaction among a population of individuals.Results from three approaches are reported: the tournament approach, the ecological approach, and the evolutionary approach. The evolutionary approach is the most general since all possible strategies can be taken into account. A series of theorems is presented which show: (1) the conditions under which no strategy can do any better than the population average if the others are using the reciprocal cooperation strategy of TIT FOR TAT, (2) the necessary and sufficient conditions for a strategy to be collectively stable, and (3) how cooperation can emerge from a small cluster of discriminating indiv...

To understand how groups coordinate, we study infinitely repeated N-player coordination games in the context of strategic uncertainty. In a situation where players share no common language or culture, ambiguity is always present. However, finding an adequate principle for a common language iLs not easy: a tradeoff between simplicity and efficiency has to be made. All these points are illustrated on repeated N-player coordination games on m loci. In particular, we demonstrate how a common principle can accelerate coordination. We present very simple rules that are optimal in the space of all languages for m (number of coordination loci) from 2 to 5 and for all N, the number of players. We also show that when more memory is used in the language (strategies), players may not coordinate, whereas this is never the case when players remember only the previous period.

In this paper, we present a study on games in which the payoffs are dynamic, that is the payoffs change with time, or are dependent on the strategy profiles of the players. We investigate two such games: a Language acquisition game, and the Spatial prisoner's dilemma game. While games in which the payoffs are constant have received much attention, games with dynamic payoffs have not been studied extensively in literature. We show in this paper that how such games can model real life situations closely, like acquisition of a grammar by children and evolution of culture.

A simple, evolutionary game-theoretic model yields the surprising prediction that cooperation can evolve without deliberate intention in a minimal social situation (MSS). This phenomenon was discovered in dyads by Sidowski (1957) and generalized to larger groups by Coleman, Colman, and Thomas (1990). Predictions about the multi-player minimal social situation (MMSS) remain untested. The primary objective of the proposed research is to test them.

Evolutionary spatial 2 x 2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2 x 2 games specified by a rescaled payoff matrix with two parameteres. Each agent is governed by a binary Markovian strategy (BMS) specified by 4 conditional probabilities [p_R, p_S, p_T, p_P] that take values 0 or 1. The initial configuration consists in a random assignment of "strategists" among the 2^4= 16 possible BMS. The system then evolves within strategy space according to the simple standard rule: each agent copies the strategy of the neighbor who got the highest payoff. Besides on the payoff matrix, the dominant strategy -and the degree of cooperation- depend on i) the type of the neighborhood (von Neumann or Moore); ii) the way the cooperation state is actualized (deterministically or stochastichally); and iii) the amount of noise measured by a parameter epsilon. However a robust wi...

A simple, evolutionary game-theoretic model yields the surprising prediction that cooperation can evolve without deliberate intention in a minimal social situation (MSS). This phenomenon was discovered in dyads by Sidowski (1957) and generalized to larger groups by Coleman, Colman, and Thomas (1990). Predictions about the multi-player minimal social situation (MMSS) remain untested. The primary objective of the proposed research is to test them.

Cellular automata-lattice-like grids of interlinked cells-can be used to study system evolution. The cells are occupied by disputants with differing strategic interaction rules. After interacting, each disputant either retains its strategy or adopts that of a neighbor, depending on relative strategy success. In this article, we use networks to answer questions about strategy evolution in the game of Chicken. We identify the nodes of a network with cells of an automaton and consider nodes adjacent if they are neighboring cells in the automaton, allowing us to determine structural influences of strategy evolution.

The similarity discrimination effect occurs when a single gene or gene cluster causes its carriers to display both a variable phenotypic trait and a behavioural predisposition to cooperate preferentially with recognisably similar carriers. We distinguish this from the greenbeard effect, in which cooperation evolves through fixed phenotypic tags and genetically linked cooperative behaviour with others displaying the same tag. Our agent-based simulations show that the evolution of cooperation through similarity discrimination, in contrast to the greenbeard effect, does not depend on population viscosity or other restrictive conditions. Similarity discrimination evolves spontaneously in well mixed populations, not only in the Prisoner's Dilemma game but also across a range of different binary-choice strategic interactions, provided that agents can distinguish reliably between similar and dissimilar co-players.

Question: How can the evolution of turn-taking be explained in species without language? Features of model: Using a genetic algorithm incorporating mutation and crossover, we studied noisy decision making in three repeated two-player games in which we predicted on theoretical grounds that cooperative turn-taking would evolve and three games in which we expected synchronized cooperation to evolve. Ranges of key variables: We set population size to 20, number of rounds to be played by each pair in each generation to 200, and number of evolutionary generations to 2000, and we repeated each simulation 10 times to check the stability of the results. Results: Cooperative turn-taking and (unexpectedly) a form of double turn-taking evolved in the alternation games, and joint cooperation evolved in the synchronization games. We propose a mechanism to explain how cooperative turn-taking can evolve mechanically, even without communication or insight, as it did in our simulations.

Question: How can the evolution of turn-taking be explained in species without language? Features of model: Using a genetic algorithm incorporating mutation and crossover, we studied noisy decision making in three repeated two-player games in which we predicted on theoretical grounds that cooperative turn-taking would evolve and three games in which we expected synchronized cooperation to evolve. Ranges of key variables: We set population size to 20, number of rounds to be played by each pair in each generation to 200, and number of evolutionary generations to 2000, and we repeated each simulation 10 times to check the stability of the results. Results: Cooperative turn-taking and (unexpectedly) a form of double turn-taking evolved in the alternation games, and joint cooperation evolved in the synchronization games. We propose a mechanism to explain how cooperative turn-taking can evolve mechanically, even without communication or insight, as it did in our simulations.

this problem using simulations. We find (1) that the most successful strategies involve a limited period of assessment followed by a stable relationship in which fights are avoided and (2) that the duration of assessment depends both on the costliness of fighting and on the difference between the animals' RHPs. Along with our direct work on modeling and simulations, we develop extensive software to facilitate further testing; it is available at https: //bitbucket.org/CameronLHall/dominancesharingassessmentmatlab/.

Question: How can the evolution of turn-taking be explained in species without language? Features of model: Using a genetic algorithm incorporating mutation and crossover, we studied noisy decision making in three repeated two-player games in which we predicted on theoretical grounds that cooperative turn-taking would evolve and three games in which we expected synchronized cooperation to evolve. Ranges of key variables: We set population size to 20, number of rounds to be played by each pair in each generation to 200, and number of evolutionary generations to 2000, and we repeated each simulation 10 times to check the stability of the results. Results: Cooperative turn-taking and (unexpectedly) a form of double turn-taking evolved in the alternation games, and joint cooperation evolved in the synchronization games. We propose a mechanism to explain how cooperative turn-taking can evolve mechanically, even without communication or insight, as it did in our simulations.

Emergence phenomena in an evolving system seem to be tied to the appearance of dynamic processes that are new with respect to their quality and unpredictable on the basis of the initial characteristic of the system. For this reason it is difficult to model emergence phenomena because the model in use may suddenly become inadequate to lay out new dynamical manifestations and therefore the true system identity.
In this work we try to build up a metamodel describing some emergence phenomena during the evolution of the dynamic organism-environment system. By means of a genetic algorithm we realized a complex system of artificial agents interacting while solving a spatial version of the Iterated Prisoner’s Dilemma (Axelrod,1984; Axelrod and Dion, 1988).

Computational Game Theory is a way to study and evaluate behaviors using game theory models, via agent-based computer simulations. One of the most known example of this approach is the famous Classical Iterated Prisoner's Dilemma (CIPD). It has been popularized by Axelrod in the beginning of the eighties and had led him to set up a successful Theory of Cooperation. This use of simulations has always been a challenging application of computer science, and of agent-based approaches, in particular to Social Sciences. It may be viewed as Empirical Game Theory. These kind of approach is often necessary since, in the general case, classical analytical ones do not give suitable results. These tools are also often used when full game-theoretic analysis is intractable. The usual method to evaluate behaviors consists in the collection of strategies, through open contests, and the confrontation of all of them as in a sport championship. Then it becomes, or at least seems to become, easy to evaluate and compare the efficiency of these behaviors. Evaluating strategies can however not be done efficiently without the insurance that algorithms used are well formed and that they can not introduce bias in their computation. It can not be done without tools able to prevent or, at least, measure deviation from the object of the study. Unfortunately people using such simulations often do not take care seriously about all those aspects, because they are not aware of it, and sometimes because they are. We will try to show effects of bad simulations practice on the simplest example. We show methodological issues which have to be taken care of, or avoided in order to prevent trouble in simulation results interpretation. Based on some simple illustration, we exhibit two kinds of bias that could be introduced. We classify them as voluntary or involuntary mistakes. The former ones can be explained by poor design of experimentations whereas the latter can defeat the purpose of the evaluation using simple ideas of agreement and cooperation. We also show the implications on interpretations and conclusions that such errors may produce. We state that scoring/ranking methods are part of the game, and as such have to be described with the game. Many points described may seem to be widely known. We think that with the growth of interest of such methods they have to be detailed and exposed clearly.

A supergame is modeled in which two agents play a game repeatedly and while the finiteness of the repetitions is common knowledge, the number of repetitions is not. Such games can yield non-standard results. This is illustrated with the Prisoner's Dilemma where a cooperative outcome is shown to be possible. * I have benefited from a seminar at the Indian Statistical Institute, Delhi, and from some comments of Debraj Ray.

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Evolutionary spatial 2 × 2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2 × 2 games specified by a rescaled payoff matrix with two parameteres. Each agent is governed by a binary Markovian strategy (BMS) specified by 4 conditional probabilities [p R , p S , p T , p P ] that take values 0 or 1. The initial configuration consists in a random assignment of "strategists" among the 2 4 = 16 possible BMS. The system then evolves within strategy space according to the simple standard rule: each agent copies the strategy of the neighbor who got the highest payoff. Besides on the payoff matrix, the dominant strategy-and the degree of cooperationdepend on i) the type of the neighborhood (von Neumann or Moore); ii) the way the cooperation state is actualized (deterministically or stochastichally); and iii) the amount of noise measured by a parameter ǫ. However a robust winner strategy is [1,0,1,1].

This article argues that only through permanent neutrality can both Koreas obtain their hitherto elusive flexible autonomy. The four major powers, China, Japan, Russia, and the US also stand to gain from Korea's neutrality, which reflects the changing geopolitical dynamics and structure of the international system in East Asia.

In the context of Evolutionary Game Theory, we have developed an evolutionary algorithm without an explicit fitness function or selection function. Instead players obtain energy by playing games. Clonal reproduction subject to mutation occurs when a player's energy exceeds some threshold. To avoid exponential growth of the population there is a death event that depends on population size. By tweaking with the relation between payoff and energy and with death event, we create another dilemma that a population must overcome: extinction. We demonstrate this phenomena in the Centipede game. Simulations show that if players can only play one of the two positions of this asymmetric game extinctions are common. If players are versatile and can play both positions there are no extinctions.

The object of study in game theory is the game, which is a formal model of an interactive situation. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influences the outcome. Since all players are assumed to be rational, they make choices which result in the outcome they prefer most, given what their opponents do. During their interaction, players update their beliefs based on the observed actions of other players. These updated beliefs can be an important reason for changes in foreign policy behavior. The paper therefore examines the game theory of U.S-Russia prior to the U.S 2016 Presidential election. As stated in changing Course, when Governments choose to redirect foreign Policy, surely there are influential factors reshaping its foreign policy (Charles F. Hermann, 1990). The paper holds that there is a mix of internal causes and exogenous factors determining the course of Russian foreign policy and the Russian-U.S engagement.

The aim of this paper is to ask the question whether the relations between North Korea and South Korea follow the premises of stimulus-response theory and thus are driven by reciprocity, or whether bullying strategy suits better to explain the relations between two Korean states. The presented data shows that reciprocating strategy was prevailing pattern of relations between Seoul and Pyongyang since the end of 1980s till 2013, thus supporting the empirical relevance of the stimulus-response theory. The existence of  eciprocity-based strategies in inter-Korean relations has been revealed, both in their confrontational and cooperational formulation, whilst higher reciprocity was found in cooperative relations.
Noteworthy, North Korean cooperative actions were of a milder character than South Korean ones, whilst South Korea did not respond by such strong confrontational actions, as were sent to it from the North. The results of the research are not significant only for theoretical level, but also for the policy-recommendation. The implication for practical politics is that states intending to increase the level of cooperation with North Korea should adopt the reciprocating strategy in its cooperative form. This approach must be adopted in the long-term perspective, as North Korea is sensitive to incoming impulses and is ready to switch from cooperation to confrontation right away.

The similarity discrimination effect occurs when a single gene or gene cluster causes its carriers to display both a variable phenotypic trait and a behavioural predisposition to cooperate preferentially with recognisably similar carriers. We distinguish this from the greenbeard effect, in which cooperation evolves through fixed phenotypic tags and genetically linked cooperative behaviour with others displaying the same tag. Our agent-based simulations show that the evolution of cooperation through similarity discrimination, in contrast to the greenbeard effect, does not depend on population viscosity or other restrictive conditions. Similarity discrimination evolves spontaneously in well mixed populations, not only in the Prisoner's Dilemma game but also across a range of different binary-choice strategic interactions, provided that agents can distinguish reliably between similar and dissimilar co-players. (A.M. Colman), lb155@le.ac.uk (L. Browning), bdp5@le.ac.uk (B.D. Pulford).

Properties of cooperation's probability function in Prisoner`s Dilemma have impact on evolution of game. Basic model defines that probability of cooperation depends linearly, both on the player's altruism and the co-player's reputation. I propose modification of activation function to smooth one (hyperbolic tangent with scaling parameter a, which corresponds to its shape) and observe three phases for different range of a. (1) For small a, strategies seem to randomly change in time and situation of mixed choices (one cooperate and second defect) dominate. (2) For medium a, players choose only one strategy for given period of time (the common state can switch to opposite one with some probability). (3) For large a, mixed strategy (once defect, once cooperate) is coexisting with common strategies and no change is allowed. I believe that proposed function characterizes better socio-economical phenomena and especially phase 1 and 2 contain most of human behavior.

Pavlov was proposed as a leading strategy for realizing cooperation because it dominates over a long period in evolutionary computer simulations of the Iterated Prisoners' Dilemma. However, our numerical calculations reveal that Pavlov and also any other cooperative strategy are not evolutionarily stable among all stochastic strategies with memory of only one previous move. We propose simple learning based on reinforcement. The learner changes its internal state, depending on an evaluation of whether the score in the previous round is larger than a critical value (aspiration level), which is genetically fixed. The current internal state decides the learner's move, but we found that the aspiration level determines its final behavior. The cooperative variant, having an intermediate aspiration level, is not an evolutionarily stable strategy (ESS) when evaluation is binary (good or bad). However, when the evaluation is quantified some cooperative variants can invade not only All-C, Tit-For-Tat (TFT), and Pavlov but also noncooperative variants with different aspiration levels. Moreover, they establish robust cooperation, which is evolutionarily stable against invasion by All-C, All-D, TFT, Pavlov, and noncooperative variants, and they receive a high score even when the error rate is high. Our results suggest that mutual cooperation can be maintained when players have a primitive learning ability.

Oligopolistic pricing decisions -in which the choice variable is not dichotomous as in the simple prisoner's dilemma but continuous -have been modeled as a generalized prisoner's dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtain an effective generalization of Rapoport's Tit for Tat for the three-person repeated game. Holland's genetic algorithm and Axelrod's representation of contingent strategies provide a means of generating new strategies in the computer, through machine learning, without outside submissions.

O LIGOPOLISTIC pricing decisions-in which the choice variable is not dichotomous as in the simple Prisoner's Dilemma but continuous-have been modeled as a Generalized Prisoner's Dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtain an effective generalization of Rapoport's Tit for Tat for the threeperson repeated game. Holland's genetic algorithm and Axelrod's representation of contingent strategies provide a means of generating new strategies in the computer, through machine learning, without outside submissions.

Evolution of game strategies is studied in the Erroneous Iterated Prisoner's Dilemma game, in which a player sometimes decides on an erroneous action contrary to his own strategy. Erroneous games of this kind have been known to lead to the evolution of a variety of strategies. This paper describes genetic fusion modeling as a particular source of new strategies. Successive actions are chosen according to strategies having finite memory capacity, and strategy algorithms are elaborated by genetic fusion. Such a fusion process introduces a rhizome structure in a genealogy tree. Emergence of module strategies functions as innovative source of new strategies. How the extinction of strategies and module evolution leads to ESS-free open-ended evolution is also discussed.

Win-stay, lose-shift strategies in repeated games are based on an aspiration level. Amove is repeated if and only if the outcome, in the previous round, was satisficing in the sense that the payoff was at least as high as the aspiration level. We investigate the conditions under which adaptive mechanisms acting on the aspiration level (selection, for instance, or learning)

This article describes computer simulations in which pairs of "individuals" in large groups played a prisoners' dilemma game. The individual's choice to cooperate or not was determined by 1 of 3 simple heuristics: tit-for-tat; win-stay, lose-change; or win-cooperate, lose-defect. Wins and losses were determined through the comparison of a play's outcome with the average outcome of the individual's neighbors. The results revealed qualitative differences between smalland large groups. Furthermore, the prevalence of cooperation in the population depended in predictable ways on the heuristic used, the values of the payoff matrix, and the details of the social comparison process that framed the outcomes as wins or losses. 131 132

Game theory is extensively used in economics to predict the best strategies in an evolutionary process of buying/selling, bargaining or in stock market. Many game solvers in the literature use simulation or even experimental games (pay the players). In general simulation takes a huge time and experimental games are very expensive. In this paper, we model the 2 · 2 non-symmetric game and the 3 · 3 symmetric game as finite, state dependent quasi-birth-and-death processes. We propose solution procedures based on the block Gaussian elimination for the 2 · 2 game and the block Gauss-Seidel iteration method for the 3 · 3 game. Our solver is a powerful tool that gives a probability distribution on the set of strategies available in the game, which helps to identify the best strategies. Furthermore, our game solver is very effective in terms of time and cost. We provide some illustrative examples.

Studies aimed at explaining the evolution of phenotypic traits have often solely focused on fitness considerations, ignoring underlying mechanisms. In recent years, there has been an increasing call for integrating mechanistic perspectives in evolutionary considerations, but it is not clear whether and how mechanisms affect the course and outcome of evolution. To study this, we compare four mechanistic implementations of two well-studied models for the evolution of cooperation, the Iterated Prisoner's Dilemma (IPD) game and the Iterated Snowdrift (ISD) game. Behavioural strategies are either implemented by a 1 : 1 genotype-phenotype mapping or by a simple neural network. Moreover, we consider two different scenarios for the effect of mutations. The same set of strategies is feasible in all four implementations, but the probability that a given strategy arises owing to mutation is largely dependent on the behavioural and genetic architecture. Our individual-based simulations show that this has major implications for the evolutionary outcome. In the ISD, different evolutionarily stable strategies are predominant in the four implementations, while in the IPD each implementation creates a characteristic dynamical pattern. As a consequence, the evolved average level of cooperation is also strongly dependent on the underlying mechanism. We argue that our findings are of general relevance for the evolution of social behaviour, pleading for the integration of a mechanistic perspective in models of social evolution.

Studies aimed at explaining the evolution of phenotypic traits have often solely focused on fitness considerations, ignoring underlying mechanisms. In recent years, there has been an increasing call for integrating mechanistic perspectives in evolutionary considerations, but it is not clear whether and how mechanisms affect the course and outcome of evolution. To study this, we compare four mechanistic implementations of two well-studied models for the evolution of cooperation, the Iterated Prisoner's Dilemma (IPD) game and the Iterated Snowdrift (ISD) game. Behavioural strategies are either implemented by a 1 : 1 genotype-phenotype mapping or by a simple neural network. Moreover, we consider two different scenarios for the effect of mutations. The same set of strategies is feasible in all four implementations, but the probability that a given strategy arises owing to mutation is largely dependent on the behavioural and genetic architecture. Our individual-based simulations show that this has major implications for the evolutionary outcome. In the ISD, different evolutionarily stable strategies are predominant in the four implementations, while in the IPD each implementation creates a characteristic dynamical pattern. As a consequence, the evolved average level of cooperation is also strongly dependent on the underlying mechanism. We argue that our findings are of general relevance for the evolution of social behaviour, pleading for the integration of a mechanistic perspective in models of social evolution.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival-the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.

We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pair-wise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This restriction creates new difficulties for most existing algorithms. The complexity of bribery and manipulation are well studied, almost always assuming deterministic information about votes and results. We assume that for candidates i and j the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for cup, challenge, and round robin competitions ranging from polynomial time to NP PP . This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.