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Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results

Author(s):Tassos Patokos
Journal: Games
Publisher:
Abstract
| Pages: 1-25
The paper presents an evolutionary model, based on the assumption that agents may revise their current strategies if they previously failed to attain the maximum level of potential payoffs. We offer three versions of this reflexive mechanism, each one of which describes a distinct type: spontaneous agents, rigid players, and ‘satisficers’. We use simulations to examine the performance of these types. Agents who change their strategies relatively easily tend to perform better in coordination games, but antagonistic games generally lead to more favorable outcomes if the individuals only change their strategies when disappointment from previous rounds surpasses some predefined threshold.

Examining Monotonicity and Saliency Using Level-k Reasoning in a Voting Game

Author(s):Anna Bassi -- Kenneth C. Williams
Journal: Games
Publisher:
Abstract
| Pages: 26-52
This paper presents an experiment that evaluates the effect of financial incentives and complexity in political science voting experiments. To evaluate the effect of complexity we adopt a level-k reasoning model concept. This model by Nagel [1] postulates that players might be of different types, each corresponding to the level of reasoning in which they engage. Furthermore, to postulate the effect of financial incentives on subjects’ choice, we used the Quantal Response Equilibrium (QRE) concept. In a QRE, players’ decisions are noisy, with the probability of playing a given strategy increasing in its expected payoff. Hence, the choice probability is a function of the magnitude of the financial incentives. Our results show that low complexity promotes the highest degree of level-k strategic reasoning in every payment treatment. Standard financial incentives are enough to induce equilibrium behavior, and the marginal effect of extra incentives on equilibrium behavior seems to be negligible. High complexity, instead, decreases the rate of convergence to equilibrium play. With a sufficiently high complexity, increasing payoff amounts does promote more strategic behavior in a significant manner. Our results show with complex voting games, higher financial incentives are required for the subjects to exert the effort needed to complete the task.

Schelling, von Neumann, and the Event that Didn’t Occur

Author(s):Alexander J. Field
Journal: Games
Publisher:
Abstract
| Pages: 53-89
Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper.

Sequential Rationality in Continuous No-Limit Poker

Author(s):Thomas W. L. Norman
Journal: Games
Publisher:
Abstract
| Pages: 92-96
Newman’s (1959, Operations Research, 7, 557–560) solution for a variant of poker with continuous hand spaces and an unlimited bet size is modified to incorporate sequential rationality.

Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities

Author(s):Anat Lerner -- Rica Gonen
Journal: Games
Publisher:
Abstract
| Pages: 97-115
We characterize the efficiency space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto-optimal combinatorial auctions in a model with two players and k nonidentical items. We examine a model with multidimensional types, private values and quasilinear preferences for the players with one relaxation: one of the players is subject to a publicly known budget constraint. We show that if it is publicly known that the valuation for the largest bundle is less than the budget for at least one of the players, then Vickrey-Clarke-Groves (VCG) uniquely fulfills the basic properties of being deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal. Our characterization of the efficient space for deterministic budget constrained combinatorial auctions is similar in spirit to that of Maskin 2000 for Bayesian single-item constrained efficiency auctions and comparable with Ausubel and Milgrom 2002 for non-constrained combinatorial auctions.

Two-Dimensional Effort in Patent-Race Games and Rent-Seeking Contests: The Case of Telephony

Author(s):João Ricardo Faria -- Franklin G. Mixon Jr. -- Steven B. Caudill -- Samantha J. Wineke
Journal: Games
Publisher:
Abstract
| Pages: 116-126
Using the political-economic history of the development of telephony during the 1870s as a backdrop, this paper studies a two-player Tullock contest that includes both research effort (R&D) and legal effort (i.e., rent-seeking effort). The two types of efforts complement each other and positively influence the payoff of the contest. We assume that legal effort affects the prize value, increasing the winner’s prospective rents, and research effort impacts the probability of winning the contest. The results of the model break new ground in showing that research effort is a function of legal effort, wherein research effort increases with rent-seeking effort. The model also shows the existence of a strategic equivalence between rent seeking and patent races.

The Seawall Bargaining Game

Author(s):Rémy Delille -- Jean-Christophe Pereau
Journal: Games
Publisher:
Abstract
| Pages: 127-139
Agents located from downstream to upstream along an estuary and exposed to a flooding risk have to invest in facilities like a seawall (or dike). As the benefits of that local public good increase along the estuary, upstream agents have to bargain for monetary compensation with the most downstream agent in exchange for more protection effort. The paper analyses different bargaining protocols and determines the conditions under which agents are better off. The results show that upstream agents are involved in a chicken game when they have to bargain with the most downstream agent.

Acknowledgement to Reviewers of Games in 2013

Author(s):Games Editorial Office
Journal: Games
Publisher:
Abstract
| Pages: 90-91
The editors of Games would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2013. [...]  

Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play

Author(s):Kristian Lindgren -- Vilhelm Verendel
Journal: Games
Publisher:
Abstract
| Pages: 1-20
The finitely repeated Prisoners’ Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A game-theoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicator-mutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The ”Convincer” strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the ”Follower” strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicator-mutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate.
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