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Population Games, Stable Games, and Passivity

Author(s):Michael J. Fox -- Jeff S. Shamma
Journal: Games
Publisher:
Abstract
| Pages: 561-583
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.

Of Coordinators and Dictators: A Public Goods Experiment

Author(s):Jürgen Fleiß -- Stefan Palan
Journal: Games
Publisher:
Abstract
| Pages: 584-607
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.

Bimodal Bidding in Experimental All-Pay Auctions

Author(s):Christiane Ernst -- Christian Thöni
Journal: Games
Publisher:
Abstract
| Pages: 608-623
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.

Strategic Voting in Heterogeneous Electorates: An Experimental Study

Author(s):Marcelo Tyszler -- Arthur Schram
Journal: Games
Publisher:
Abstract
| Pages: 624-647
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.

An Adaptive Learning Model in Coordination Games

Author(s):Naoki Funai
Journal: Games
Publisher:
Abstract
| Pages: 648-669
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.

The Optimality of Team Contracts

Author(s):Mehmet Barlo -- Ayça Özdoğan
Journal: Games
Publisher:
Abstract
| Pages: 670-689
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.

The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings

Author(s):Rica Gonen -- Anat Lerner
Journal: Games
Publisher:
Abstract
| Pages: 690-710
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.

A Game-Theoretic Analysis of Baccara Chemin de Fer

Author(s):Stewart N. Ethier -- Carlos Gámez
Journal: Games
Publisher:
Abstract
| Pages: 711-737
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.

Auctioning the Right to Play Ultimatum Games and the Impact on Equilibrium Selection

Author(s):Jason Shachat -- J. Todd Swarthout
Journal: Games
Publisher:
Abstract
| Pages: 738-753
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.
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