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Games, Volume 4, Issue 1 (March 2013), Pages 1-143

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Research

Open AccessArticle Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play
Games 2013, 4(1), 1-20; doi:10.3390/g4010001
Received: 5 September 2012 / Revised: 15 November 2012 / Accepted: 21 December 2012 / Published: 4 January 2013
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Abstract
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
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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. Full article
Open AccessArticle An Equilibrium Analysis of Knaster’s Fair Division Procedure
Games 2013, 4(1), 21-37; doi:10.3390/g4010021
Received: 19 October 2012 / Revised: 8 January 2013 / Accepted: 8 January 2013 / Published: 18 January 2013
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Abstract
In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding
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In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, ex-post, the equilibrium allocation is still efficient but may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully—i.e., the mechanism is ex-ante fair. Full article
(This article belongs to the Special Issue Mechanism Design)
Open AccessArticle Nash Implementation in an Allocation Problem with Single-Dipped Preferences
Games 2013, 4(1), 38-49; doi:10.3390/g4010038
Received: 25 November 2012 / Revised: 10 January 2013 / Accepted: 15 January 2013 / Published: 30 January 2013
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Abstract
In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this
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In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable. Full article
Open AccessArticle Tacit Collusion under Fairness and Reciprocity
Games 2013, 4(1), 50-65; doi:10.3390/g4010050
Received: 25 September 2012 / Revised: 28 January 2013 / Accepted: 29 January 2013 / Published: 7 February 2013
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Abstract
This paper departs from the standard profit-maximizing model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards their competitors. A reciprocal firm responds to unkind behavior of rivals with unkind actions (negative reciprocity), while at the same
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This paper departs from the standard profit-maximizing model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards their competitors. A reciprocal firm responds to unkind behavior of rivals with unkind actions (negative reciprocity), while at the same time, it responds to kind behavior of rivals with kind actions (positive reciprocity). We find that collusion is easier to sustain when firms have a concern for reciprocity towards competing firms provided that they consider collusive prices to be kind and punishment prices to be unkind. Thus, reciprocity concerns among firms can have adverse welfare consequences for consumers. Full article
Open AccessArticle Hierarchical Bayesian Analysis of Biased Beliefs and Distributional Other-Regarding Preferences
Games 2013, 4(1), 66-88; doi:10.3390/g4010066
Received: 22 November 2012 / Revised: 28 January 2013 / Accepted: 29 January 2013 / Published: 19 February 2013
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Abstract
This study investigates the relationship between an actor’s beliefs about others’ other-regarding (social) preferences and her own other-regarding preferences, using an “avant-garde” hierarchical Bayesian method. We estimate two distributional other-regarding preference parameters, α and β, of actors using incentivized choice data in binary
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This study investigates the relationship between an actor’s beliefs about others’ other-regarding (social) preferences and her own other-regarding preferences, using an “avant-garde” hierarchical Bayesian method. We estimate two distributional other-regarding preference parameters, α and β, of actors using incentivized choice data in binary Dictator Games. Simultaneously, we estimate the distribution of actors’ beliefs about others α and β, conditional on actors’ own α and β, with incentivized belief elicitation. We demonstrate the benefits of the Bayesian method compared to it’s hierarchical frequentist counterparts. Results show a positive association between an actor’s own (α; β ) and her beliefs about average(α; β) in the population. The association between own preferences and the variance in beliefs about others’ preferences in the population, however, is curvilinear for α and insignificant for β. These results are partially consistent with the cone effect [1,2] which is described in detail below. Because in the Bayesian-Nash equilibrium concept, beliefs and own preferences are assumed to be independent, these results cast doubt on the application of the Bayesian-Nash equilibrium concept to experimental data. Full article
Open AccessArticle Group Size, Coordination, and the Effectiveness of Punishment in the Voluntary Contributions Mechanism: An Experimental Investigation
Games 2013, 4(1), 89-105; doi:10.3390/g4010089
Received: 16 November 2012 / Revised: 29 January 2013 / Accepted: 5 February 2013 / Published: 19 February 2013
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Abstract
We examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the marginal per capita return (MPCR), i.e. the return to each participant
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We examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the marginal per capita return (MPCR), i.e. the return to each participant from each dollar that is contributed, is held constant. Moreover, the efficiency gains from the punishment mechanism are significantly higher in the 40-participant than in the four-participant treatment. This is true despite the coordination problems inherent in an institution relying on decentralized individual punishment decisions in the context of a larger group. It reflects increased per capita expenditures on punishment that offset the greater coordination difficulties in the larger group. However, if the marginal group return (MGR), i.e. the return to the entire group of participants, stays constant, resulting in an MPCR that shrinks with group size, no such offset occurs and punishment loses much but not all of its effectiveness at encouraging voluntary contributions to a public good. Efficiency is not significantly different from the small-group treatment. Full article
Open AccessArticle Divorce Costs and Marital Dissolution in a One-to-One Matching Framework With Nontransferable Utilities
Games 2013, 4(1), 106-124; doi:10.3390/g4010106
Received: 14 December 2012 / Revised: 23 February 2013 / Accepted: 4 March 2013 / Published: 20 March 2013
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Abstract
In this paper, we use a two-period one-to-one matching model with incomplete information to examine the effect of changes in divorce costs on marital dissolution. Each individual who has a nontransferable expected utility about the quality of each potential marriage decides whether to
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In this paper, we use a two-period one-to-one matching model with incomplete information to examine the effect of changes in divorce costs on marital dissolution. Each individual who has a nontransferable expected utility about the quality of each potential marriage decides whether to marry or to remain single at the beginning of the first period. Individuals married in the first period learn the qualities of their marriages at the beginning of the second period and then decide whether to stay married or to unilaterally divorce. We show that, for any society, there exist matching environments where the probability of the marital dissolution does not reduce divorce costs under gender-optimal matching rules. In such environments, an allocation effect of divorce costs with an ambiguous sign outweighs an incentive effect that is always negative. We also show that these results may also arise under stable matching rules that are not gender optimal. Full article
(This article belongs to the Special Issue Games and Matching Markets)
Open AccessArticle Two Pricing Mechanisms in Sponsored Search Advertising
Games 2013, 4(1), 125-143; doi:10.3390/g4010125
Received: 6 October 2012 / Revised: 29 January 2013 / Accepted: 19 February 2013 / Published: 20 March 2013
Cited by 3 | PDF Full-text (580 KB) | HTML Full-text | XML Full-text
Abstract
Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two
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Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP. Full article
(This article belongs to the Special Issue Mechanism Design)

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