Achieving Cooperation in a Minimally Constrained Environment

Ssrn Electronic Journal, 2003

When a prisoner's-dilemma-like game is repeated any finite number of times, the only equilibrium outcome is the one in which all players defect in all periods. However, if cooperation among the players changes their perception of the game by making defection increasingly less attractive, then players may be willing to cooperate in late periods in which unilateral defection has become unprofitable. In this case, cooperation may also be attainable in the first period, since defection then can effectively be punished by cessation of cooperation by all the other players. In this paper, we explore this possibility and consider conditions guaranteeing the players' willingness to cooperate also in the middle periods, in which defection is more profitable than later on, and at the same time, punishments are less effective than at the beginning. These conditions are sufficient for the existence of an equilibrium in which players cooperate in all periods. * We would like to thank Eliakim Katz, with whom the ideas presented in this paper were originally conceived. a Personal homepage: http://faculty.biu.ac.il/~weissa1 be hollow, since, in any subgame perfect equilibrium at least, defection in the last period takes place anyway. In fact, even without the perfection requirement, there can be no last period in which any player cooperates with positive probability. Therefore, the probability of cooperation ever occurring is zero. In this paper, we diverge from the classical model by allowing the players' preferences over the possible outcomes in each period to depend on history. Specifically, we assume that a history of cooperation makes defection an increasingly less attractive alternative as time progresses. One possible interpretation for such an effect of past cooperation on the willingness to cooperate is that defection carries a moral cost, which is greater the longer the history of cooperation. Empirical support for the idea that history may affect people's behavior in prisoner's-dilemma-like games can be found in the work of , which is described in Section 2.

This paper addresses the issue of emergence of robust cooperation among self-interested agents interacting in N-player social dilemma games. A series of graphs are created each exhibiting a different level of community structure; we show the influence that community structure has on the emergence of cooperation. A strategy set that represent a form of generalised tit-for-tat is used. Two forms of uncertainty in the environment are also modelled. The influence of the game length is also explored.

Unpublished paper, Santa Fe Institute, 2007

The n-player public goods game, the basic model of decentralized social cooperation in non-market settings, has a unique Nash equilibrium in which all players defect. The Folk Theorem asserts that near-Pareto-optimal payoffs can be supported if the game is indefinitely repeated and the discount factor is sufficiently near unity. This paper advances the view that the Folk Theorem does not explain why or how individuals cooperate in these settings. First, with imperfect public signaling, the Folk Theorem's implication that ...

Lecture Notes in Computer Science, 2003

We introduce a very complex game based on an approximate solution of a NP-hard problem, so that the probability of victory grows monotonically, but of an unknown amount, with the resources each player employs. We formulate this model in the computational learning framework and focus on the problem of computing a confidence interval for the losing probability. We deal with the problem of reducing the width of this interval under a given threshold in both batch and on-line modality. While the former leads to a feasible polynomial complexity, the on-line learning strategy may get stuck in an indeterminacy trap: the more we play the game the broader becomes the confidence interval. In order to avoid this indeterminacy we organise in a better way the knowledge, introducing the notion of virtual game to achieve the goal efficiently. Then we extend the one-player to a team mode game. Namely, we improve the success of a team by redistributing the resources among the players and exploiting their mutual cooperation to treat the indeterminacy phenomenon suitably.

Computational and Mathematical Organization Theory, 2008

The problem of understanding the conditions under which cooperation or altruism can be sustained between interacting selfish entities is a fundamental issue in both biology and the social sciences. In recent years, there has been an explosion of work utilising agent-based computer simulation to explore novel mechanisms for cooperation. This surge was probably kick-started by the famous "computer tournaments" and related work of Robert Axelrod (1984). Predating this, of course, there is a large body of mathematical game theoretic analysis following in the tradition established by von Neumann and Morgenstern (1944). Historically, this latter approach has tended towards unrealistically strong assumptions concerning the rationality and knowledge of actors. More recently, refinements have addressed systems with slightly less strong assumptions.

Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner's dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups. evolutionary game theory | alliances | public goods game | volunteer's dilemma | cooperation C ooperation among self-interested individuals is generally difficult to achieve (1-3), but typically the free rider problem is aggravated even further when groups become large (4-9). In small communities, cooperation can often be stabilized by forms of direct and indirect reciprocity (10-17). For large groups, however, it has been suggested that these mechanisms may turn out to be ineffective, as it becomes more difficult to keep track of the reputation of others and because the individual influence on others diminishes (4-8). To prevent the tragedy of the commons and to compensate for the lack of individual control, many successful communities have thus established central institutions that enforce mutual cooperation (18-22).

Review of Economic Studies, 2018

We study environments in which agents are randomly matched to play a Prisoner’s Dilemma, and each player observes a few of the partner’s past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.

Proceedings of the 22nd international conference on Machine learning - ICML '05, 2005

Learning algorithms often obtain relatively low average payoffs in repeated general-sum games between other learning agents due to a focus on myopic best-response and one-shot Nash equilibrium (NE) strategies. A less myopic approach places focus on NEs of the repeated game, which suggests that (at the least) a learning agent should possess two properties. First, an agent should never learn to play a strategy that produces average payoffs less than the minimax value of the game. Second, an agent should learn to cooperate/compromise when beneficial. No learning algorithm from the literature is known to possess both of these properties. We present a reinforcement learning algorithm (M-Qubed) that provably satisfies the first property and empirically displays (in self play) the second property in a wide range of games.

2005

Abstract We analyze a cooperation game and a coordination game in an evolutionary environment. Agents make noisy observations of opponent's propensity to play dove, called reputation, and form preferences over opponents based on their reputation. A game takes place when two agents agree to play. Socially optimal cooperation is evolutionarily stable when reputation perfectly reflects propensity to cooperate. With some reputation noise, there will be at least some cooperation.

2010

Experimental and Monte Carlo methods were used to test theoretical predictions about adaptive learning of cooperative responses without awareness in minimal social situations-games in which the payoffs to players depend not on their own actions but exclusively on the actions of other group members. In Experiment 1, learning occurred slowly over 200 rounds in a dyadic minimal social situation but not in multiplayer groups. In Experiments 2, 3, and 4, learning occurred rarely in multiplayer groups, even when players were informed that they were interacting strategically and were allowed to communicate with one another but were not aware of the game's payoff structure. Monte Carlo simulation suggested that players approach minimal social situations using a noisy version of the win-stay, lose-shift decision rule, deviating from the deterministic rule less frequently after rewarding than unrewarding rounds.