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on Game Theory |
| By: | Burkhard Schipper (Department of Economics, University of California Davis) |
| Abstract: | It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be "evolutionary stable" or that "could learn itself". Rather, a player has an incentive to strategically teach such a learning opponent in order secure at least the Stackelberg leader payoff. The impossibility result remains intact when restricted to the classes of generic games, two-player games, potential games, games with strategic complements or 2x2 games, in which learning is known to be "nice". More generally, it also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizable outcomes, iterated admissible outcomes, or minimal curb sets. A possibility result restricted to "strategically trivial" games fails if some generic games outside this class are considered as well. |
| Keywords: | Learning in games, learning heuristics, learning rules, interactive learning, uncoupled learning, meta-learning, reputation, Nash equilibrium, correlated equilibrium, rationalizability, iterated admissibility, minimal curb sets, dominance solvable games, common interest games |
| JEL: | C72 C73 |
| Date: | 2015–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:15-1&r=gth |
| By: | Musegaas, M. (Tilburg University, Center For Economic Research); Borm, P.E.M. (Tilburg University, Center For Economic Research); Quant, M. (Tilburg University, Center For Economic Research) |
| Abstract: | In this paper we introduce three-valued simple games as a natural extension<br/>of simple games. While simple games are used to evaluate single voting systems, three-valued simple games offer the opportunity for a simultaneous analysis of two different voting systems within the same parliamentary body. This paper analyzes the core and the Shapley value of three-valued simple games. Using the concept of vital players, the vital core is constructed and we show that the vital core is a subset of the core. The Shapley value is characterized on the class of all three-valued simple games. The model is applied to evaluate the relative influence of countries within the current EU-28 Council. |
| Keywords: | simple games; three-valued simple games; core; Shapley value |
| JEL: | C71 C44 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:473afd5c-99b1-4073-888f-2006e20fbf5f&r=gth |
| By: | Tamas Solymosi (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences); Balazs Sziklai (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences) |
| Abstract: | We provide a new modus operandi for the computation of the nucleolus in cooperative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and dually saturated coalitions determine both the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two sets are related with the existing characterization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself. We conclude with a sample computation of the nucleolus of bankruptcy games - the shortest of its kind. |
| Keywords: | Cooperative game theory, Nucleolus, Characterization sets |
| JEL: | C71 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1512&r=gth |
| By: | Jo Laban Peryman (RMIT University, Melbourne); David Kelsey (Department of Economics, University of Exeter) |
| Abstract: | We run experiments with a stag hunt and bargaining coordination game. Using a between-subjects design, we vary the identity of the opponent between someone of the same culture or a different culture. The idea is to see whether cultural norms or identity play a part in coordination decisions. We compare the responses of British and Asian students at the University of Exeter and show the cultural identity of the opponent by physical appearance. The players appear to use cultural stereotypes to predict behaviour, especially in the bargaining game which may require more strategic thought than the stag hunt game. In particular, the British act in way that indicates they believe the Asians will behave more cautiously than other British. According to our results, the stereotype of Asians being cautious is misleading. |
| Keywords: | culture,identity, norms, coordination, bargaining |
| JEL: | C29 C71 C72 Z13 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:1505&r=gth |
| By: | Goto, Masahiro; Kojima, Fuhito; Kurata, Ryoji; Tamura, Akihisa; Yokoo, Makoto |
| Abstract: | In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and ``more fair'' than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and ``less wasteful'' than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains. |
| Keywords: | two-sided matching, many-to-one matching, market design, matching with contracts, matching with constraints, strategyproofness,deferred acceptance |
| JEL: | C78 D61 D63 |
| Date: | 2015–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64000&r=gth |
| By: | Daniel Huppmann; Sauleh Siddiqui |
| Abstract: | We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity. |
| Keywords: | binary Nash game, non-cooperative equilibrium, compensation, incentive compatibility, electricity market, power market, uplift payments |
| JEL: | C72 C61 L13 L94 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1475&r=gth |
| By: | Edward Cartwright; Anna Stepanova |
| Abstract: | We contrast and compare three ways of predicting efficiency in a forced contribution threshold public good game. The three alternatives are based on ordinal potential, quantal response and impulse balance theory. We report an experiment designed to test the respective predictions and find that impulse balance gives the best predictions. A simple expression detailing when enforced contributions result in high or low efficiency is provided. |
| Keywords: | Public good; threshold; impulse balance theory; quantal response; forced contribution; ordinal potential |
| JEL: | C72 H41 C92 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:1506&r=gth |
| By: | Sara le Roux (Department of Economics, Oxford Brookes University); David Kelsey (Department of Economics, University of Exeter) |
| Abstract: | This paper studies the impact of ambiguity in the best shot and weakest link models of public good provision. The models are ?rst analysed theoretically. Then we conduct experiments to study how ambiguity affects behaviour in these games. We test whether subjects? perception of ambiguity differs between a local opponent and a foreign one. We fi?nd that an ambiguity safe strategy, is often chosen by subjects. This is compatible with the hypothesis that ambiguity aversion infl?uences behaviour in games. Subjects tend to choose contributions above (resp. below) the Nash equilibrium in the Best Shot (resp. Weakest Link) model. |
| Keywords: | Public goods; Ambiguity; Choquet expected utility; strategic complements; weakest link; best shot. |
| JEL: | C72 C91 D03 D81 H41 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:1506&r=gth |
| By: | Alexander L. Brown (Texas A&M University, Department of Economics); Rodrigo A. Velez (Texas A&M University, Department of Economics) |
| Abstract: | In experimental partnership dissolution problems with complete information, the divide-and-choose mechanism is significantly superior to the winner's-bid-auction. The performance of divide-and-choose is mainly affected by reciprocity issues and not by bounded rationality. The performance of the winner's-bid-auction is significantly affected by bounded rationality. Contrary to theoretical predicitions divide-and-choose exhibits no first-mover bias. |
| Keywords: | experimental economics; no-envy; divide-and-choose; winner's-bid auction; behavioral mechanism design |
| JEL: | C91 D63 C72 |
| URL: | http://d.repec.org/n?u=RePEc:txm:wpaper:20141106-10001&r=gth |
| By: | Paul Pezanis-Christou (School of Economics, University of Adelaide); Werner Güth (LUISS, 32 Viale Romania, 00197 Rome, Italy. Frankfurt School of Finance and Management, 9-11 Sonnemann St., 60314 Frankfurt, Germany. Max Planck Institute for Research on Collective Goods, 10 Kurt-Schumacher St., 53113 Bonn, Germany.) |
| Abstract: | The risk-neutral equilibrium bidding strategy for first-price auctions with independent private values is justified without assuming a well-defined Bayesian game. Bidders, aware of their own value, assume the private values to be linearly related. The latter, however, are independent and identically distributed, and this is only known by Nature. Allowing for arbitrary linear common value beliefs, and assuming optimal bidding for such beliefs we derive the unique evolutionarily stable conjectural belief and justify risk neutral bidding in a new and hopefully innovative way. |
| Keywords: | Evolutionarily stable strategy, indirect evolution, first-price auction, independent private values, symmetric Bayes-Nash equilibrium. |
| JEL: | C7 D4 D8 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2015-13&r=gth |
| By: | Jingfeng Lu (Department of Economics, National University of Singapore); Zhewei Wang (School of Economics, Shandong University) |
| Abstract: | In this paper, we identify a set of axioms that is necessary and sufficient for axiomatizing the reverse nested lottery contest proposed by Fu, Lu and Wang (2014), which is the "mirror image" of the conventional nested lottery contest of Clark and Riis (1996). This paper thus provides an axiomatic underpinning for the reverse model, which which further reveals the connections and differences between the two (conventional and reverse) multi-prize contest models. |
| JEL: | C72 D72 D74 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:shn:wpaper:2015-03&r=gth |
| By: | Bell, Peter N |
| Abstract: | Exploration is a costly activity that helps a business improve their understanding of a potential mineral deposit. Yet, even with strong exploration results, the business faces uncertainty over the value of the mine. I model this situation as a game of chance. The game starts by giving an agent an asset with random value and ends when the agent chooses to accept the random value or reject it and receive zero instead. The agent can pay to learn more about the asset’s value as many times as they like before they end the game, but no amount of exploration will remove all uncertainty. I provide a decision rule for the agent based on an interval estimate for the asset value and analyze performance of the decision rule in a simulation experiment. |
| Keywords: | Mineral exploration, game theory, learning, simulation. |
| JEL: | C02 C44 C63 C70 D83 Q39 |
| Date: | 2015–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62159&r=gth |
| By: | Carlos A. Manzanares; Ying Jiang; Patrick Bajari |
| Abstract: | In this paper, we propose a method for finding policy function improvements for a single agent in high-dimensional Markov dynamic optimization problems, focusing in particular on dynamic games. Our approach combines ideas from literatures in Machine Learning and the econometric analysis of games to derive a one-step improvement policy over any given benchmark policy. In order to reduce the dimensionality of the game, our method selects a parsimonious subset of state variables in a data-driven manner using a Machine Learning estimator. This one-step improvement policy can in turn be improved upon until a suitable stopping rule is met as in the classical policy function iteration approach. We illustrate our algorithm in a high-dimensional entry game similar to that studied by Holmes (2011) and show that it results in a nearly 300 percent improvement in expected profits as compared with a benchmark policy. |
| JEL: | C44 C73 L1 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21124&r=gth |
| By: | Maroš Servátka (University of Canterbury); Daniel Woods |
| Abstract: | This paper tests Psychological Forward Induction in the Lost Wallet Game, in an attempt to explain an empirical puzzle observed by Dufwenberg & Gneezy (2000) that the size of the outside option forgone by the first mover does not affect the behavior of the second mover. This is puzzling as Psychological Forward Induction and other theories predict that raising the outside option will increase the reward provided by the second mover to the first mover for foregoing the outside option. Our experiment tests whether the second movers update their beliefs after observing their paired first movers’ decision by eliciting beliefs with different second mover knowledge of first mover decision, depending on treatment. We find that second movers do update their beliefs conditional on receiving information on the first mover’s action, supporting Psychological Forward Induction. |
| Keywords: | beliefs, experiment, guilt aversion, lost wallet game, psychological forward induction |
| JEL: | C70 C91 |
| Date: | 2015–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:15/09&r=gth |
| By: | Patrick Bajari; Victor Chernozhukov; Han Hong; Denis Nekipelov |
| Abstract: | In this paper, we study the identification and estimation of a dynamic discrete game allowing for discrete or continuous state variables. We first provide a general nonparametric identification result under the imposition of an exclusion restriction on agent payoffs. Next we analyze large sample statistical properties of nonparametric and semiparametric estimators for the econometric dynamic game model. We also show how to achieve semiparametric efficiency of dynamic discrete choice models using a sieve based conditional moment framework. Numerical simulations are used to demonstrate the finite sample properties of the dynamic game estimators. An empirical application to the dynamic demand of the potato chip market shows that this technique can provide a useful tool to distinguish long term demand from short term demand by heterogeneous consumers. |
| JEL: | C01 C14 C7 C73 L0 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21125&r=gth |
| By: | Shuo Liu |
| Abstract: | We study the effect of public information on collective decision-making in a committee with members of both common and conflicting interests. We show that the set of preferences that allow for the existence of an informative voting equilibrium can be heavily restricted by the presence of a public signal, regardless of the size of the committee and the choice of the voting threshold value. What’s worse, the presence of the public information introduces an inefficient equilibrium which robustly exists across different voting rules. To mitigate the harmful effect of the public information, we propose to use a class of more flexible voting rules, whose threshold values de- pend on both the precision and the realization of the public signal, that may restore the informative voting equilibrium. In particular, in a standard setting with common interest agents, the contingent voting rule that we construct not only always restores the informative voting equilibrium but also achieves full informational efficiency. |
| Keywords: | Strategic voting, collective decision-making, public information, committee design, optimal voting rule |
| JEL: | D72 D82 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:191&r=gth |
| By: | Martin Pollrich (Humboldt-Universitaet zu Berlin) |
| Abstract: | For optimal audit contracts the principle of maximum deterrence applies: penalties imposed by the contract are either zero or at their maximal level. Additionally, an imperfect audit technology which reveals the agent’s type only with an error makes the principal worse off. In this paper I show that both statements are no longer true when the principal cannot commit to an audit strategy. Both intermediate penalties and imperfect audits facilitate the creation of incentives for the principal to carry out an audit. Creation Date: 2015-03-18 |
| Keywords: | Auditing, limited commitment, contract theory |
| JEL: | D82 D86 C72 |
| URL: | http://d.repec.org/n?u=RePEc:bdp:wpaper:2015004&r=gth |