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2427 KiB

Open AccessArticle

Commitment to Cooperation and Peer Punishment: Its Evolution

by Tatsuya Sasaki, Isamu Okada, Satoshi Uchida and Xiaojie Chen

Games 2015, 6(4), 574-587; https://doi.org/10.3390/g6040574 - 3 Nov 2015

Cited by 39 | Viewed by 9570

Theoretical and empirical studies have generally weighed the effect of peer punishment and pool punishment for sanctioning free riders separately. However, these sanctioning mechanisms often pose a puzzling tradeoff between efficiency and stability in detecting and punishing free riders. Here, we combine the [...] Read more.

Theoretical and empirical studies have generally weighed the effect of peer punishment and pool punishment for sanctioning free riders separately. However, these sanctioning mechanisms often pose a puzzling tradeoff between efficiency and stability in detecting and punishing free riders. Here, we combine the key aspects of these qualitatively different mechanisms in terms of evolutionary game theory. Based on the dilemmatic donation game, we introduce a strategy of commitment to both cooperation and peer punishment. To make the commitment credible, we assume that those willing to commit have to make a certain deposit. The deposit will be refunded as long as the committers faithfully cooperate in the donation game and punish free riders and non-committers. It turns out that the deposit-based commitment offers both the efficiency of peer punishment and the stability of pool punishment and that the replicator dynamics lead to transitions of different systems: pool punishment to commitment to peer punishment. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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471 KiB

Open AccessArticle

Cooperate without Looking in a Non-Repeated Game

by Christian Hilbe, Moshe Hoffman and Martin A. Nowak

Games 2015, 6(4), 458-472; https://doi.org/10.3390/g6040458 - 30 Sep 2015

Cited by 11 | Viewed by 7938

Abstract

We propose a simple model for why we have more trust in people who cooperate without calculating the associated costs. Intuitively, by not looking at the payoffs, people indicate that they will not be swayed by high temptations to defect, which makes them [...] Read more.

We propose a simple model for why we have more trust in people who cooperate without calculating the associated costs. Intuitively, by not looking at the payoffs, people indicate that they will not be swayed by high temptations to defect, which makes them more attractive as interaction partners. We capture this intuition using a simple four-stage game. In the first stage, nature draws the costs and benefits of cooperation according to a commonly-known distribution. In the second stage, Player 1 chooses whether or not to look at the realized payoffs. In the third stage, Player 2 decides whether to exit or let Player 1 choose whether or not to cooperate in the fourth stage. Using backward induction, we provide a complete characterization for when we expect Player 1 to cooperate without looking. Moreover, we show with numerical simulations how cooperating without looking can emerge through simple evolutionary processes. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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1214 KiB

Open AccessArticle

Indirect Reciprocity with Optional Interactions and Private Information

by Jason Olejarz, Whan Ghang and Martin A. Nowak

Games 2015, 6(4), 438-457; https://doi.org/10.3390/g6040438 - 30 Sep 2015

Cited by 22 | Viewed by 6685

Abstract

We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is [...] Read more.

We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright–Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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507 KiB

Open AccessArticle

Evolution of Decisions in Population Games with Sequentially Searching Individuals

by Tadeas Priklopil and Krishnendu Chatterjee

Games 2015, 6(4), 413-437; https://doi.org/10.3390/g6040413 - 29 Sep 2015

Viewed by 5688

Abstract

In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. [...] Read more.

In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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335 KiB

Open AccessArticle

Strong Migration Limit for Games in Structured Populations: Applications to Dominance Hierarchy and Set Structure

by Dhaker Kroumi and Sabin Lessard

Games 2015, 6(3), 318-346; https://doi.org/10.3390/g6030318 - 7 Sep 2015

Cited by 7 | Viewed by 5464

Abstract

In this paper, we deduce a condition for a strategy S1 to be more abundant on average at equilibrium under weak selection than another strategy S2 in a population structured into a finite number of colonies of fixed proportions as the population size [...] Read more.

In this paper, we deduce a condition for a strategy S1 to be more abundant on average at equilibrium under weak selection than another strategy S2 in a population structured into a finite number of colonies of fixed proportions as the population size tends to infinity. It is assumed that one individual reproduces at a time with some probability depending on the payoff received in pairwise interactions within colonies and between colonies and that the offspring replaces one individual chosen at random in the colony into which the offspring migrates. It is shown that an expected weighted average equilibrium frequency of S1 under weak symmetric strategy mutation between S1 and S2 is increased by weak selection if an expected weighted payoff of S1 near neutrality exceeds the corresponding expected weighted payoff of S2. The weights are given in terms of reproductive values of individuals in the different colonies in the neutral model. This condition for S1 to be favoured by weak selection is obtained from a strong migration limit of the genealogical process under neutrality for a sample of individuals, which is proven using a two-time scale argument. The condition is applied to games between individuals in colonies with linear or cyclic dominance and between individuals belonging to groups represented by subsets of a given set. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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1459 KiB

Open AccessArticle

The Evolvability of Cooperation under Local and Non-Local Mutations

by Alexander J. Stewart and Joshua B. Plotkin

Games 2015, 6(3), 231-250; https://doi.org/10.3390/g6030231 - 23 Jul 2015

Cited by 14 | Viewed by 7988

Abstract

We study evolutionary dynamics in a population of individuals engaged in pairwise social interactions, encoded as iterated games. We consider evolution within the space of memory-1strategies, and we characterize all evolutionary robust outcomes, as well as their tendency to evolve under the evolutionary [...] Read more.

We study evolutionary dynamics in a population of individuals engaged in pairwise social interactions, encoded as iterated games. We consider evolution within the space of memory-1strategies, and we characterize all evolutionary robust outcomes, as well as their tendency to evolve under the evolutionary dynamics of the system. When mutations are restricted to be local, as opposed to non-local, then a wider range of evolutionary robust outcomes tend to emerge, but mutual cooperation is more difficult to evolve. When we further allow heritable mutations to the player’s investment level in each cooperative interaction, then co-evolution leads to changes in the payoff structure of the game itself and to specific pairings of robust games and strategies in the population. We discuss the implications of these results in the context of the genetic architectures that encode how an individual expresses its strategy or investment. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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658 KiB

Open AccessArticle

Fairness and Trust in Structured Populations

by Corina E. Tarnita

Games 2015, 6(3), 214-230; https://doi.org/10.3390/g6030214 - 20 Jul 2015

Cited by 17 | Viewed by 6503

Abstract

Classical economic theory assumes that people are rational and selfish, but behavioral experiments often point to inconsistent behavior, typically attributed to “other regarding preferences.” The Ultimatum Game, used to study fairness, and the Trust Game, used to study trust and trustworthiness, have been [...] Read more.

Classical economic theory assumes that people are rational and selfish, but behavioral experiments often point to inconsistent behavior, typically attributed to “other regarding preferences.” The Ultimatum Game, used to study fairness, and the Trust Game, used to study trust and trustworthiness, have been two of the most influential and well-studied examples of inconsistent behavior. Recently, evolutionary biologists have attempted to explain the evolution of such preferences using evolutionary game theoretic models. While deterministic evolutionary game theoretic models agree with the classical economics predictions, recent stochastic approaches that include uncertainty and the possibility of mistakes have been successful in accounting for both the evolution of fairness and the evolution of trust. Here I explore the role of population structure by generalizing and expanding these existing results to the case of non-random interactions. This is a natural extension since such interactions do not occur randomly in the daily lives of individuals. I find that, in the limit of weak selection, population structure increases the space of fair strategies that are selected for but it has little-to-no effect on the optimum strategy played in the Ultimatum Game. In the Trust Game, in the limit of weak selection, I find that some amount of trust and trustworthiness can evolve even in a well-mixed population; however, the optimal strategy, although trusting if the return on investment is sufficiently high, is never trustworthy. Population structure biases selection towards strategies that are both trusting and trustworthy trustworthy and reduces the critical return threshold, but, much like in the case of fairness, it does not affect the winning strategy. Further considering the effects of reputation and structure, I find that they act synergistically to promote the evolution of trustworthiness. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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210 KiB

Open AccessArticle

What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma

by Ethan Akin

Games 2015, 6(3), 175-190; https://doi.org/10.3390/g6030175 - 25 Jun 2015

Cited by 37 | Viewed by 7258

Abstract

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving [...] Read more.

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

8772 KiB

Open AccessArticle

Should Law Keep Pace with Society? Relative Update Rates Determine the Co-Evolution of Institutional Punishment and Citizen Contributions to Public Goods

by Daria Roithmayr, Alexander Isakov and David Rand

Games 2015, 6(2), 124-149; https://doi.org/10.3390/g6020124 - 3 Jun 2015

Cited by 9 | Viewed by 7614

Abstract

Until recently, theorists considering the evolution of human cooperation have paid little attention to institutional punishment, a defining feature of large-scale human societies. Compared to individually-administered punishment, institutional punishment offers a unique potential advantage: the ability to control how quickly legal rules of [...] Read more.

Until recently, theorists considering the evolution of human cooperation have paid little attention to institutional punishment, a defining feature of large-scale human societies. Compared to individually-administered punishment, institutional punishment offers a unique potential advantage: the ability to control how quickly legal rules of punishment evolve relative to social behavior that legal punishment regulates. However, at what rate should legal rules evolve relative to society to maximize compliance? We investigate this question by modeling the co-evolution of law and cooperation in a public goods game with centralized punishment. We vary the rate at which States update their legal punishment strategy relative to Citizens’ updating of their contribution strategy and observe the effect on Citizen cooperation. We find that when States have unlimited resources, slower State updating lead to more Citizen cooperation: by updating more slowly, States force Citizens to adapt to the legal punishment rules. When States depend on Citizens to finance their punishment activities, however, we find evidence of a ‘Goldilocks’ effect: optimal compliance is achieved when legal rules evolve at a critical evolutionary rate that is slow enough to force citizens to adapt, but fast enough to enable states to quickly respond to outbreaks of citizen lawlessness. Full article

(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)

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