Games2015, 6(3), 231-250; doi:10.3390/g6030231 - published 23 July 2015 Show/Hide Abstract
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 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.
Games2015, 6(3), 214-230; doi:10.3390/g6030214 - published 20 July 2015 Show/Hide Abstract
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 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.
Games2015, 6(3), 191-213; doi:10.3390/g6030191 - published 3 July 2015 Show/Hide Abstract
Abstract: We consider auctions with price externality where all bidders derive utility from the winning price, such as charity auctions. In addition to the benefit to the winning bidder, all bidders obtain a benefit that is increasing in the winning price. Theory makes two predictions in such settings: First, individual bids will be increasing in the multiplier on the winning price. Second, individual bids will not depend on the number of other bidders. Empirically, we find no evidence that increasing the multiplier increases individual bids in a systematic way, but we find that increasing the number of bidders does. An analysis of individual bidding functions reveals that bidders underweight the incentives to win and overweight the incentives to lose.
Games2015, 6(3), 175-190; doi:10.3390/g6030175 - published 25 June 2015 Show/Hide Abstract
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 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.
Games2015, 6(2), 161-174; doi:10.3390/g6020161 - published 19 June 2015 Show/Hide Abstract
Abstract: We set up a rich bilateral bargaining model with four salient points (disagreement point, ideal point, reference point, and tempered aspirations point), where the disagreement point and the utility possibilities frontier are endogenously determined. This model allows us to compare two bargaining solutions that use reference points, the Gupta-Livne solution and the tempered aspirations solution, in terms of Pareto efficiency in a strategic framework. Our main result shows that the weights solutions place on the disagreement point do not directly imply a unique efficiency ranking in this bargaining problem with a reference point. In particular, the introduction of a reference point brings one more degree of freedom to the model which requires also the difference in the weights placed on the reference point to be considered in reaching an efficiency ranking.
Games2015, 6(2), 150-160; doi:10.3390/g6020150 - published 3 June 2015 Show/Hide Abstract
Abstract: This paper analyzes the dynamic stability of moral codes in a two population trust game. Guided by a moral code, members of one population, the Trustors, are willing to punish members of the other population, the Trustees, who defect. Under replicator dynamics, adherence to the moral code has unstable oscillations around an interior Nash Equilibrium (NE), but under smoothed best response dynamics we obtain convergence to Quantal Response Equilibrium (QRE).