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Games, Volume 4, Issue 4 (December 2013), Pages 561-794

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Research

Open AccessArticle Population Games, Stable Games, and Passivity
Games 2013, 4(4), 561-583; doi:10.3390/g4040561
Received: 4 April 2013 / Revised: 3 September 2013 / Accepted: 26 September 2013 / Published: 7 October 2013
Cited by 9 | PDF Full-text (162 KB) | HTML Full-text | XML Full-text
Abstract
The class of “stable games”, introduced by Hofbauer and Sandholm in 2009, has the attractive property of admitting global convergence to equilibria under many evolutionary dynamics. We show that stable games can be identified as a special case of the feedback-system-theoretic notion [...] Read more.
The class of “stable games”, introduced by Hofbauer and Sandholm in 2009, has the attractive property of admitting global convergence to equilibria under many evolutionary dynamics. We show that stable games can be identified as a special case of the feedback-system-theoretic notion of a “passive” dynamical system. Motivated by this observation, we develop a notion of passivity for evolutionary dynamics that complements the definition of the class of stable games. Since interconnections of passive dynamical systems exhibit stable behavior, we can make conclusions about passive evolutionary dynamics coupled with stable games. We show how established evolutionary dynamics qualify as passive dynamical systems. Moreover, we exploit the flexibility of the definition of passive dynamical systems to analyze generalizations of stable games and evolutionary dynamics that include forecasting heuristics as well as certain games with memory. Full article
(This article belongs to the Special Issue Advances in Evolutionary Game Theory and Applications)
Open AccessArticle Of Coordinators and Dictators: A Public Goods Experiment
Games 2013, 4(4), 584-607; doi:10.3390/g4040584
Received: 17 July 2013 / Revised: 11 September 2013 / Accepted: 8 October 2013 / Published: 10 October 2013
Cited by 4 | PDF Full-text (355 KB) | HTML Full-text | XML Full-text
Abstract
We experimentally investigate whether human subjects are willing to give up individual freedom in return for the benefits of improved coordination. We conduct a modified iterated public goods game in which subjects in each period first decide which of two groups to [...] Read more.
We experimentally investigate whether human subjects are willing to give up individual freedom in return for the benefits of improved coordination. We conduct a modified iterated public goods game in which subjects in each period first decide which of two groups to join. One group employs a voluntary contribution mechanism, the other group an allocator contribution mechanism. The setup of the allocator mechanism differs between two treatments. In the coordinator treatment, the randomly selected allocator can set a uniform contribution for all group members, including herself. In the dictator treatment, the allocator can choose different contributions for herself and all other group members. We find that subjects willingly submit to authority in both treatments, even when competing with a voluntary contribution mechanism. The allocator groups achieve high contribution levels in both treatments. Full article
Open AccessArticle Bimodal Bidding in Experimental All-Pay Auctions
Games 2013, 4(4), 608-623; doi:10.3390/g4040608
Received: 17 July 2013 / Revised: 19 September 2013 / Accepted: 19 September 2013 / Published: 11 October 2013
Cited by 1 | PDF Full-text (257 KB) | HTML Full-text | XML Full-text
Abstract
We report results from experimental first-price, sealed-bid, all-pay auctions for a good with a common and known value. We observe bidding strategies in groups of two and three bidders and under two extreme information conditions. As predicted by the Nash equilibrium, subjects [...] Read more.
We report results from experimental first-price, sealed-bid, all-pay auctions for a good with a common and known value. We observe bidding strategies in groups of two and three bidders and under two extreme information conditions. As predicted by the Nash equilibrium, subjects use mixed strategies. In contrast to the prediction under standard assumptions, bids are drawn from a bimodal distribution: very high and very low bids are much more frequent than intermediate bids. Standard risk preferences cannot account for our results. Bidding behavior is, however, consistent with the predictions of a model with reference dependent preferences as proposed by the prospect theory. Full article
Open AccessArticle Strategic Voting in Heterogeneous Electorates: An Experimental Study
Games 2013, 4(4), 624-647; doi:10.3390/g4040624
Received: 23 August 2013 / Revised: 17 October 2013 / Accepted: 28 October 2013 / Published: 11 November 2013
Cited by 2 | PDF Full-text (402 KB) | HTML Full-text | XML Full-text
Abstract
We study strategic voting in a setting where voters choose from three options and Condorcet cycles may occur. We introduce in the electorate heterogeneity in preference intensity by allowing voters to differ in the extent to which they value the three options. [...] Read more.
We study strategic voting in a setting where voters choose from three options and Condorcet cycles may occur. We introduce in the electorate heterogeneity in preference intensity by allowing voters to differ in the extent to which they value the three options. Three information conditions are tested: uninformed, in which voters know only their own preference ordering and the own benefits from each option; aggregate information, in which in addition they know the aggregate realized distribution of the preference orderings and full information, in which they also know how the relative importance attributed to the options are distributed within the electorate. As a general result, heterogeneity seems to decrease the level of strategic voting in our experiment compared to the homogenous preference case that we study in a companion paper. Both theoretically and empirically (with data collected in a laboratory experiment), the main comparative static results obtained for the homogenous case carry over to the present setting with preference heterogeneity. Moreover, information about the realized aggregate distribution of preferences seems to be the element that best explains observed differences in voting behavior. Additional information about the realized distribution of preference intensity does not yield significant further changes. Full article
(This article belongs to the Special Issue Laboratory Experimental Testing of Political Science Models)
Open AccessArticle An Adaptive Learning Model in Coordination Games
Games 2013, 4(4), 648-669; doi:10.3390/g4040648
Received: 15 September 2013 / Revised: 4 November 2013 / Accepted: 7 November 2013 / Published: 15 November 2013
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Abstract
In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in normal form games with strict Nash equilibria. In the model, each player assigns subjective payoff assessments to his own actions, where [...] Read more.
In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in normal form games with strict Nash equilibria. In the model, each player assigns subjective payoff assessments to his own actions, where the assessment of each action is a weighted average of its past payoffs, and chooses the action which has the highest assessment. After receiving a payoff, each player updates the assessment of his chosen action in an adaptive manner. We show almost sure convergence to a Nash equilibrium under one of the following conditions: (i) that, at any non-Nash equilibrium action profile, there exists a player who receives a payoff, which is less than his maximin payoff; (ii) that all non-Nash equilibrium action profiles give the same payoff. In particular, the convergence is shown in the following games: the battle of the sexes game, the stag hunt game and the first order statistic game. In the game of chicken and market entry games, players may end up playing the action profile, which consists of each player’s unique maximin action. Full article
Open AccessArticle The Optimality of Team Contracts
Games 2013, 4(4), 670-689; doi:10.3390/g4040670
Received: 11 April 2013 / Revised: 31 October 2013 / Accepted: 11 November 2013 / Published: 18 November 2013
Cited by 1 | PDF Full-text (484 KB) | HTML Full-text | XML Full-text
Abstract
This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others’ effort levels and draft enforceable side-contracts [...] Read more.
This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others’ effort levels and draft enforceable side-contracts on effort levels and realized returns. Standard constraints, resulting in incentive contracts, fail to ensure implementability, and we examine centralized collusion-proof contracts and decentralized team contracts, as well. We prove that the principal may restrict attention to team contracts whenever returns from the project satisfy a mild monotonicity condition. Full article
(This article belongs to the Special Issue Contract Theory)
Open AccessArticle The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings
Games 2013, 4(4), 690-710; doi:10.3390/g4040690
Received: 19 June 2013 / Revised: 2 November 2013 / Accepted: 7 November 2013 / Published: 18 November 2013
Cited by 4 | PDF Full-text (399 KB) | HTML Full-text | XML Full-text
Abstract
We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known [...] Read more.
We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices. Full article
Open AccessArticle A Game-Theoretic Analysis of Baccara Chemin de Fer
Games 2013, 4(4), 711-737; doi:10.3390/g4040711
Received: 13 September 2013 / Revised: 6 November 2013 / Accepted: 6 November 2013 / Published: 18 November 2013
Cited by 1 | PDF Full-text (523 KB) | HTML Full-text | XML Full-text
Abstract
Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 x 288 matrix game, which was solved [...] Read more.
Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 x 288 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only his own total, baccara is a 2 x 2484 matrix game, which was solved by Downton and Lockwood in 1975 for d = 1, 2, . . . , 8. Assuming that cards are dealt without replacement from a d-deck shoe and that each of Player and Banker sees the composition of his own two-card hand, baccara is a 25 x 2484 matrix game, which is solved herein for every positive integer d. Full article
Open AccessArticle Auctioning the Right to Play Ultimatum Games and the Impact on Equilibrium Selection
Games 2013, 4(4), 738-753; doi:10.3390/g4040738
Received: 23 September 2013 / Revised: 25 October 2013 / Accepted: 11 November 2013 / Published: 27 November 2013
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Abstract
We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the [...] Read more.
We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equilibrium, and auction prices emerge supporting this equilibrium by the principle of forward induction. With random assignment, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. While Nash equilibria with low offers are observed, the subgame perfect Nash equilibrium never is. Full article
Open AccessArticle External Pressure on Alliances: What Does the Prisoners’ Dilemma Reveal?
Games 2013, 4(4), 754-775; doi:10.3390/g4040754
Received: 15 September 2013 / Revised: 13 November 2013 / Accepted: 18 November 2013 / Published: 10 December 2013
PDF Full-text (222 KB) | HTML Full-text | XML Full-text
Abstract
Prompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use [...] Read more.
Prompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival’s competition, either with the alliance or with the individual partners. We show that, while strong external pressure on both partners can cause Ally-Ally to become a Nash equilibrium for the two-player Prisoners’ Dilemma, weak or asymmetric pressure that plays on the partners’ differing objectives can undermine the alliance. As well as providing new insights into how allies should respond if the alliance is to continue, this also illustrates how a third party can most effectively cause the alliance to become unsustainable. We create a new game theoretic framework, adding value to existing theory and the practice of alliance formation and sustainability. Full article
Open AccessArticle Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study
Games 2013, 4(4), 776-794; doi:10.3390/g4040776
Received: 16 September 2013 / Revised: 5 December 2013 / Accepted: 12 December 2013 / Published: 18 December 2013
Cited by 3 | PDF Full-text (305 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
In this paper, we claim that agents confronting with new interactive situations apply behavioral heuristics that drastically reduce the problem complexity either by neglecting the other players’ incentives, or by restricting attention to subsets of “salient” outcomes. We postulate that these heuristics [...] Read more.
In this paper, we claim that agents confronting with new interactive situations apply behavioral heuristics that drastically reduce the problem complexity either by neglecting the other players’ incentives, or by restricting attention to subsets of “salient” outcomes. We postulate that these heuristics are sensitive to the manipulation of those features that can be modified without altering the (Nash) equilibrium structure of the game. We call these features “descriptive”. We test experimentally the effect of these descriptive features on both choice behavior and cross-game similarity perception. Analysis of individual choices confirms our hypotheses, and suggests that non-equilibrium choices may derive from simplified mental models of the game structure, rather than from heterogeneous beliefs or limited iterative thinking. In addition, subjects tend to behave similarly in games sharing similar descriptive features, regardless of their strategic structure. Full article

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