|
on Game Theory |
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Issue of 2014‒05‒09
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Hannu Salonen (Department of Economics, University of Turku) |
| Abstract: | We study non-cooperative link formation games in which players have to decide how much to invest in relationships with other players. A link between two players is formed, if and only if both make a positive investment. The cost of forming a link can be interpreted as the opportunity cost of privacy. We analyze the existence of pure strategy equilibria and the resulting network structures with tractable specifications of utility functions. Sufficient conditions for the existence of reciprocal equilibria are given and the corresponding network structure is analyzed. Pareto optimal and strongly stable network structures are studied. It turns out that such networks are often complete. |
| Keywords: | link formation games, reciprocal equilibrium, complete network |
| JEL: | C72 D43 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp89&r=gth |
| By: | Jason Shachat; J. Todd Swarthout |
| Abstract: | We conduct an experiment in which we auction the scarce rights to play the Proposer and Responder positions in subsequent ultimatum games. As a control treatment, we randomly allocate these rights and then charge exogenous participation fees according to the auction price sequences observed in the auction treatment. With endogenous selection into ultimatum games via auctions, we find that play converges to a session-specific Nash equilibrium and auction prices emerge which support this equilibrium by the principle of forward induction. With random assignment and exogenous participation fees, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. The Nash equilibrium observed within a session results in low ultimatum game offers, but the subgame perfect Nash equilibrium is never observed. |
| Keywords: | Ultimatum Bargaining; Auction; Forward Induction |
| JEL: | C92 C78 D44 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002056&r=gth |
| By: | Jason Shachat; J. Todd Swarthouty; Lijia Wei |
| Abstract: | We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects' play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects' play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects' latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not self-enforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states. |
| Keywords: | Mixed Strategy, Nash Equilibrium, Experiment, Hidden Markov Model |
| JEL: | C92 C72 C10 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002021&r=gth |
| By: | Llerena Garrés, Francesc; Nuñez, Marina (Núñez Oliva) |
| Abstract: | On the domain of general assignment games (with possible reservation prices) the core is axiomatized as the unique solution satisfying two consistency principles: projection consistency and derived consistency. Also, an axiomatic characterization of the nucleolus is given as the unique solution that satisfies derived consistency and equal maximum complaint between groups. As a consequence, we obtain a geometric characterization of the nucleolus. Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his / her optimally matched partner equals the maximum amount that he / she can receive from this partner, also remaining inside the core. We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions. Key words: cooperative games, assignment game, core, nucleolus |
| Keywords: | Jocs cooperatius, 33 - Economia, |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/228403&r=gth |
| By: | Chenghu Ma |
| Abstract: | This paper is to provide a theoretical foundation of incomplete contract in an extensive game of multi-agent interaction. It aims to explain why rational agents may agree upon incomplete contracts even though it is costless to sign a complete one. It is argued that an incomplete contract creates strategic uncertainty. If agents’ attitudes toward uncertainty are not neutral, then an incomplete contract as final solution can be the consequence of common knowledge of rationality. This paper assumes that all agents are uncertainty averse in a sense of Gilboa and Schmeidler (1989); and that agents can form coalitions as part of strategic play. All these are embedded into a newly proposed equilibrium solution concept for extensive form game of perfect information. |
| Keywords: | uncertainty aversion, strategic uncertainty, coalitionformation, stability and core-criterion. |
| JEL: | C70 C71 C72 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001970&r=gth |
| By: | Jason Shachat; J. Todd Swarthout; Lijia Wei |
| Abstract: | We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice. |
| Keywords: | Mixed Strategy; Nash Equilibrium; Experiment; Hidden Markov Model |
| JEL: | C92 C72 C10 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002048&r=gth |
| By: | Mitri Kitti (Department of Economics, University of Turku) |
| Abstract: | This paper considers policies and payoffs corresponding to subgame perfect equilibrium strategies in discounted stochastic games with finitely many states. It is shown that a policy is induced by an equilibrium strategy if and only if it can be supported with the threat of reverting to the induced policy that gives the least equilibrium payoff for the deviator. It follows that the correspondence of subgame perfect equilibrium payoffs is the largest fixed-point of a correspondence-valued operator defined by the players’ incentive compatibility conditions. Moreover, the fixed-point iteration converges to the equilibrium payoff correspondence. |
| Keywords: | Subgame Perfect Equilibria in Discounted Stochastic Games |
| JEL: | C73 |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp87&r=gth |
| By: | Luca Polonio; Sibilla Di Guida; Giorgio Coricelli |
| Abstract: | We used eye-tracking to measure the dynamic patterns of visual information acquisition in twoplayers normal form games. Participants played one-shot games in which either, neither, or only oneof the players had a dominant strategy. First, we performed a mixture models cluster analysis to groupparticipants into types according to the pattern of visual information acquisition observed in a singleclass of games. Then, we predicted agents’ choices in different classes of games, and observed thatpatterns of visual information acquisition were game invariant. Our method allowed us to predictwhether the decision process would lead to equilibrium choices or not, and to attribute out-ofequilibriumresponses to limited cognitive capacities or social motives. Our results suggest theexistence of individually heterogeneous-but stable-patterns of visual information acquisition basedon subjective levels of strategic sophistication and social preferences. |
| Keywords: | game theory; strategic sophistication; social preferences; attention; eye-tracking |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/159867&r=gth |
| By: | Christian Ewerhart |
| Abstract: | This paper studies a large class of imperfectly discriminating contests, referred to as elastic contests, that induce players to either overbid a standing bid or to abstain from bidding altogether. Many common forms of contest are elastic. In any equilibrium of an elastic contest, there is complete rent dissipation for all but at most one player. This result is used to show that in any suffciently decisive anonymous standard contest, any equilibrium is an all-pay auction equilibrium. Thus, the analysis offers strong support for the robustness of the all-pay auction. The approach also delivers definite answers regarding the extent of rent dissipation in Tullock contests with intermediate values of the decisiveness parameter. |
| Keywords: | Contests, all-pay auction; rent-seeking, mixed nash equilibrium, rent dissipation |
| JEL: | C72 D45 D72 L12 |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:155&r=gth |
| By: | Jason Shachat; J. Todd Swarthout |
| Abstract: | We report results from an experiment in which humans repeatedly play one of two games against a computer program that follows either a reinforcement or an experience weighted attraction learning algorithm. Our experiment shows these learning algorithms detect exploitable opportunities more sensitively than humans. Also, learning algorithms respond to detected payoff-increasing opportunities systematically; however, the responses are too weak to improve the algorithms' payoffs. Human play against various decision maker types doesn't vary significantly. These factors lead to a strong linear relationship between the humans' and algorithms' action choice proportions that is suggestive of the algorithms' best response correspondences. |
| Keywords: | Learning, Repeated games, Experiments, Simulation |
| JEL: | C72 C92 C81 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002031&r=gth |
| By: | Yafeng Wang; Brett Graham |
| Abstract: | We propose a data-constrained generalized maximum entropy estimator for discrete sequential move games of perfect information. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and requires o simulation or assumptions about the distribution of random preference shocks. We formulate the GME estimation as a (convex) mixed-integer nonlinear optimization problem which can be easily implemented on optimization software with high-level interfaces such as GAMS. The model is identified with only weak scale and location normalizations. Monte Carlo evidence demonstrates that the estimator can perform well in moderately size samples. As an application we study the location choice of German siblings using the German Ageing Survey. |
| Keywords: | Game-Theoretic Econometric Models, Sequential-Move Game, Generalized ，Maximum Entropy, Mixed-Integer Nonlinear Programming. |
| JEL: | C01 C13 C35 C51 C72 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002036&r=gth |
| By: | Gautam Bose (School of Economics, Australian School of Business, the University of New South Wales); Lorraine Ivancic (School of Economics, Australian School of Business, the University of New South Wales); Evgenia Dechter (School of Economics, Australian School of Business, the University of New South Wales) |
| Abstract: | There is substantial experimental and empirical evidence to suggest that individual behaviour in bilateral or small-group interactions is affected by social norms. Further, social norms vary according to context. Previous research largely focuses on norms of fairness, not norms per se. We design an experiment to decouple norm-adherence from fairness. We find that (a) a group norm evolves and individuals cluster more tightly around it as they learn the average behaviour of the group, (b) actions further from this norm in a self-serving direction are less acceptable by others, and (c) when an agent is moved to a group with a different norm, s/he conforms quickly to the new norm. |
| Keywords: | group behaviour, norms, conformism, fairness, ultimatum game |
| JEL: | C72 C78 C92 Z13 |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2014-21&r=gth |
| By: | Liu, Xin |
| Abstract: | This paper analyses a game theoretic model of tax competition in a system where tax authorities are revenue optimisers and countries are differentiated by size. The model accommodates more than two countries. In equilibrium, larger countries set higher tax rates non-cooperatively. By applying the Hotelling linear model, this paper gives examples where the size effect, neighbourhood effect, and peripheral effect coexist and push up the tax rate in equilibrium. -- |
| Keywords: | tax competition,cross-border shopping,Nash equilibrium,peripheral effects |
| JEL: | H20 H71 H73 R51 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:201419&r=gth |
| By: | Tommy Andersson; Zaifu Yang; Dongmo Zhang |
| Abstract: | Price controls are used in many regulated markets and well recognized as the cause of market inefficiency. This paper examines a practical housing market in the presence of price controls and provides a solution to the problem of how houses should be efficiently allocated among agents through a system of prices. We demonstrate that the dynamic auction by Talman and Yang (2008) always finds a core allocation in finitely many iterations, thus resulting in a Pareto efficient outcome. |
| Keywords: | Ascending auction, assignment market, price control, Pareto efficiency, core. |
| JEL: | C71 D44 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:14/05&r=gth |
| By: | Jason Shachat; Lijia Tan |
| Abstract: | In reverse auctions, buyers often retain the right to bargain further concessions from the winner. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winner. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it o ers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions, calculated using a formulation of probability weighting, of the Bayesian posteriors. We show alternative models based upon risk aversion and anticipated regret can't explain these price dependencies. |
| Keywords: | Auction, Bargaining, Experiment, Subjective Posterior |
| JEL: | C34 C92 D03 D44 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002055&r=gth |
| By: | Aptus, Elias; Britz, Volker; Gersbach, Hans |
| Abstract: | We examine the impact of so-called Crisis Contracts on bank managers' risktaking incentives and on the probability of banking crises. Under a Crisis Contract, managers are required to contribute a pre-specified share of their past earnings to finance public rescue funds when a crisis occurs. This can be viewed as a retroactive tax that is levied only when a crisis occurs and that leads to a form of collective liability for bank managers. We develop a game-theoretic model of a banking sector whose shareholders have limited liability, so that society at large will suffer losses if a crisis occurs. Without Crisis Contracts, the managers' and shareholders' interests are aligned, and managers take more than the socially optimal level of risk. We investigate how the introduction of Crisis Contracts changes the equilibrium level of risk-taking and the remuneration of bank managers. We establish conditions under which the introduction of Crisis Contracts will reduce the probability of a banking crisis and improve social welfare. We explore how Crisis Contracts and capital requirements can supplement each other and we show that the efficacy of Crisis Contracts is not undermined by attempts to hedge. -- |
| Keywords: | banking crises,Crisis Contracts,excessive risk taking,banker's pay,hedging,capital requirements |
| JEL: | C79 G21 G28 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:453&r=gth |