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on Game Theory |
| By: | Radzvilas, Mantas |
| Abstract: | Orthodox game theory is often criticized for its inability to single out intuitively compelling Nash equilibria in non-cooperative games. The theory of virtual bargaining, developed by Misyak and Chater (2014) suggests that players resolve non-cooperative games by making their strategy choices on the basis of what they would agree to play if they could openly bargain. The proposed formal model of bargaining, however, has limited applicability in non-cooperative games due to its reliance on the existence of a unique non-agreement point – a condition that is not satisfied by games with multiple Nash equilibria. In this paper, I propose a model of ordinal hypothetical bargaining, called the Benefit-Equilibration Reasoning, which does not rely on the existence of a unique reference point, and offers a solution to the equilibrium selection problem in a broad class of non-cooperative games. I provide a formal characterization of the solution, and discuss the theoretical predictions of the suggested model in several experimentally relevant games. |
| Keywords: | Nash equilibrium, bargaining, equilibrium selection problem, Nash bargaining solution, correlated equilibrium, virtual bargaining, best-response reasoning |
| JEL: | C70 C71 C72 C78 |
| Date: | 2016–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:70248&r=gth |
| By: | KAYABA, Yutaka; MATSUSHIMA, Hitoshi; TOYAMA, Tomohisa |
| Abstract: | We experimentally examine repeated prisoners' dilemma with random termination, where monitoring is imperfect and private. Our estimation indicates that a significant proportion of subjects follow generous Tit-For-Tat (g-TFT) strategies, straightforward extensions of Tit-For-Tat. However, the observed retaliating policies are inconsistent with the g-TFT equilibria. Contrarily to the theory, subjects tend to retaliate more with high accuracy than with low accuracy. They tend to retaliate more than the theory predicts with high accuracy, while they tend to retaliate lesser with low accuracy. In order to describe these results as unique equilibrium, we demonstrate an alternative theory that incorporates naetand reciprocity. |
| Keywords: | Repeated Prisoner's Dilemma, Imperfect Private Monitoring, Experiments, Generous Tit-For-Tat, Behavioral Model |
| JEL: | C70 C71 C72 C73 D03 |
| Date: | 2016–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hiasdp:hias-e-23&r=gth |
| By: | Matthew Embrey (University of Sussex); Friederike Mengel (University of Essex and Maastricht University); Ronald Peeters (Maastricht University) |
| Abstract: | This paper studies whether and how strategy revision opportunities affect levels of collusion in indefinitely repeated two-player games. Consistent with standard theory, we find that such opportunities do not affect strategy choices, or collusion levels, if the game is of strategic substitutes. In contrast, there is a strong and positive effect for games of strategic complements. Revision opportunities lead to more collusion. The latter cannot be explained by renegotiation or standard risk-dominance considerations, but is consistent with a notion of fear of miscoordination based on minmax regret. |
| Keywords: | strategy revision opportunities, cooperation, repeated games, complements vs. substitutes, fear of miscoordination |
| JEL: | C73 C92 D43 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:sus:susewp:8716&r=gth |
| By: | Marilda Sotomayor |
| Abstract: | For a general coalitional game with non-transferable utility (NTU game) and a finite set of players, (N,V), Scarf (1967) proved that every balanced game has a non-empty core. Billera (1970) showed, through an example, that this condition is not always necessary when V(N) has a supremum. By using the concepts of simple outcome and Pareto simple outcome, the present paper provides a weaker condition than balancedness, which is sufficient for the non-emptiness of the core in the general case and is necessary when V(N) has a supremum. It is also necessary for any TU game. Our proof avoids the use of balancedness and specialized mathematical tools. Instead, it is elementary and only employs simple combinatorial arguments. |
| Keywords: | Core; simple payoff vector; Pareto optimal simple outcome |
| JEL: | C78 D78 |
| Date: | 2016–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2016wpecon5&r=gth |
| By: | Elena Yanovskaya (National Research University Higher School of Economics) |
| Abstract: | Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents [Moulin 2000] is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom -- self covariance -- that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom not applicable to methods for profit sharing problems |
| Keywords: | cooperative game with transferable utilities, cost/surplus sharing method, self-covariance, solution |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:127/ec/2016&r=gth |
| By: | Dimitrios Xefteris; Nicholas Ziros |
| Abstract: | This paper studies decentralized vote trading in a power-sharing system that follows the rules of strategic market games. In particular, we study a two-party election, in which prior to the voting stage voters are free to trade votes for money. Voters hold private information about both their ordinal and cardinal preferences, whereas their utilities are proportionally increasing in the vote share of their favorite party. In this framework we prove generic existence of a unique full trade equilibrium (an equilibrium in which nobody refrains from vote trading). We moreover argue that vote trading in such systems unambiguously improves voters' welfare. |
| Keywords: | vote trading, strategic market games, power sharing |
| JEL: | C72 D72 P16 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:01-2016&r=gth |
| By: | Marilda Sotomayor |
| Abstract: | We approach the roommate problem by focusing on well-behaved matchings, which are those individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. We show that the set of stable matchings is non-empty if and only if no well-behaved and unstable matching is Pareto optimal among all well-behaved matchings. The economic intuition underlying this condition is that blocking can be done so that the transactions at any well-behaved and unstable matching need not be undone as agents reach the the set of stable matchings. We also give a sufficient condition on the preferences of the agents for the non-emptiness of the set of stable matchings. New properties of economic interest are proved |
| Keywords: | Core; Stable matching; well-behaved matching; simple matching. |
| JEL: | C78 D78 |
| Date: | 2016–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2016wpecon6&r=gth |
| By: | Syngjoo Choi; Edoardo Gallo; Shachar Kariv; |
| Abstract: | This chapter surveys experimental research on networks in economics. The first part considers experiments on games played on networks. The second part discusses experimental research on markets and networks. It concludes by identifying important directions for future research. |
| Keywords: | experiments, social networks, network games, markets, coordination, public goods, cooperation, social learning, communication, trading. |
| JEL: | C91 C92 D85 L14 Z13 |
| Date: | 2015–03–17 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1551&r=gth |
| By: | Belik, Ivan (Dept. of Business and Management Science, Norwegian School of Economics); Jörnsten, Kurt (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | Methods for leader’s detection and overthrow in networks are useful tools for decision-making in many real-life cases, such as criminal networks with hidden patterns or money laundering networks. In the given research, we represent the algorithms that detect and overthrow the most influential node to the weaker positions following the greedy method in terms of structural modifications. We employed the concept of Shapley value from the area of cooperative games to measure a node’s leadership and used it as the core of the developed leader’s overthrow algorithms. The approaches are illustrated based on the trivial network structures and tested on real-life networks. The results are represented in tabular and graphical formats. |
| Keywords: | Leadership; networks analysis; Shapley value; game theory |
| JEL: | C00 C60 C61 Z13 |
| Date: | 2016–01–21 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2016_001&r=gth |
| By: | Katarina Cechlarova; Bettina Klaus; David F.Manlove |
| Abstract: | We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity, indicating the maximum number of courses and applicants they can be assigned to, respectively. We thus essentially have a many-tomany bipartite matching problem with one-sided preferences, which has applications to the assignment of students to optional courses at a university. We consider additive preferences and lexicographic preferences as two means of extending preferences over individual courses to preferences over bundles of courses. We additionally focus on the case that courses have prerequisite constraints: we will mainly treat these constraints as compulsory, but we also allow alternative prerequisites. We further study the case where courses may be corequisites. For these extensions to the basic problem, we present the following algorithmic results, which are mainly concerned with the computation of Pareto optimal matchings (POMs). Firstly, we consider compulsory prerequisites. For additive preferences, we show that the problem of finding a POM is NP-hard. On the other hand, in the case of lexicographic preferences we give a polynomial-time algorithm for finding a POM, based on the well-known sequential mechanism. However we show that the problem of deciding whether a given matching is Pareto optimal is co-NP-complete. We further prove that finding a maximum cardinality (Pareto optimal) matching is NP-hard. Under alternative prerequisites, we show that finding a POM is NP-hardfor either additive or lexicographic preferences. Finally we consider corequisites. We prove that, as in the case of compulsory prerequisites, finding a POM is NP-hard for additive preferences, though solvable in polynomial time for lexicographic preferences. In the latter case, the problem of finding a maximum cardinality POM is NP-hard and very difficult to approximate. |
| Keywords: | many-to-many matching problem, course allocation, additive / lexicographic preferences, polynomial-time algorithm, NP-hardness |
| JEL: | C63 C78 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:16.04&r=gth |
| By: | Alessandra Casella (Columbia University, NBER and CEPR); Jean-François Laslier (Paris School of Economics and CNRS); Antonin Macé (Aix-Marseille Universit´e (Aix-Marseille School of Economics), CNRS and EHESS) |
| Abstract: | In a polarized committee, majority voting disenfranchises the minority. By allowing voters to spend freely a fixed budget of votes over multiple issues, Storable Votes restores some minority power. We study a model of Storable Votes that highlights the hide-and-seek nature of the strategic game. With communication, the game replicates a classic Colonel Blotto game with asymmetric forces. We call the game without communication a decentralized Blotto game. We characterize theoretical results for this case and test both versions of the game in the laboratory. We find that, despite subjects deviating from equilibrium strategies, the minority wins as frequently as theory predicts. Because subjects understand the logic of the game – minority voters must concentrate votes unpredictably – the exact choices are of secondary importance. The result is an endorsement of the robustness of the voting rule. |
| Keywords: | Storable Votes, Polarization, Colonel Blotto, Tyranny of the Majority, Committees |
| JEL: | D71 C72 C92 |
| Date: | 2016–03–11 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:1612&r=gth |
| By: | Karagözoğlu, Emin; Kocher, Martin G. |
| Abstract: | We experimentally investigate the effect of time pressure in a rich-context, unstructured bargaining game with earned status and competing reference points. Our results show that average opening proposals, concessions, and agreed shares are very similar across different levels of time pressure. Nevertheless, as predicted, time pressure systematically influenced agreements. In particular, the likelihood of bargainers reaching the explicit reference point outcome in agreements increases with time pressure, and the likelihood of reaching the implicit reference point (equal division) in agreements decreases with time pressure. Disagreement rates and the frequency of last-moment agreements are strongly affected: the disagreement rate rises dramatically with time pressure, and last-moment agreements are significantly more frequent. This effect is explained by a stronger connection between the tension in first proposals and the final bargaining outcome under time pressure than without time pressure. |
| Keywords: | Bargaining; Disagreements; Last-moment Agreements; Reference Points; Time Pressure. |
| JEL: | C71 C91 D74 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:26642&r=gth |
| By: | Ayse Gül Mermer; Wieland Müller; Sigrid Suetens |
| Abstract: | This paper studies the effects of transparency on information transmission and decision-making theoretically and experimentally. We develop a model in which a de- cision maker seeks the advice of a better-informed adviser. Before giving advice, the adviser may choose to accept a side payment from a third party, where accepting this payment binds the advisor to give a particular recommendation, which may or may not be dishonest. Without transparency, the decision maker learns only the recom- mendation of the adviser. With transparency, the decision maker learns in addition the decision of the adviser with respect to the side payment. Prior research has shown that transparency is either ine¤ective or harmful to decisionmakers? because con?icted advisers become more dishonest in their advice. The novelty of our model is that the conflict of interest is endogeneous as the adviser can choose to decline the third-party payment. Our theoretical results predict that transparency is never harmful and may help decision makers. Our experimental results show that transparency improves the accuracy of decision making. However, we also observe that (i) while transparency clearly improves decision making when it is mandatory, the evidence in favor of a voluntary form of transparency is much weaker, and that (ii) the positive e¤ects of transparency decline over time. |
| JEL: | L13 C72 C92 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:vie:viennp:1603&r=gth |
| By: | Yutaka Kayaba (Hitotsubashi Institute for Advanced Study, Hitotsubashi University); Hitoshi Matsushima (Faculty of Economics, The University of Tokyo); Tomohisa Toyama (Division of Liberal Arts, Kogakuin University) |
| Abstract: | We experimentally examine repeated prisoners' dilemma with random termination, where monitoring is imperfect and private. Our estimation indicates that a significant proportion of subjects follow generous Tit-For-Tat (g-TFT) strategies, straightforward extensions of Tit-For-Tat. However, the observed retaliating policies are inconsistent with the g-TFT equilibria. Contrarily to the theory, subjects tend to retaliate more with high accuracy than with low accuracy. They tend to retaliate more than the theory predicts with high accuracy, while they tend to retaliate lesser with low accuracy. In order to describe these results as unique equilibrium, we demonstrate an alternative theory that incorporates naïveté and reciprocity. |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2016cf1004&r=gth |
| By: | Lars EHLERS; Dipjyoti MAJUMDAR; Debasis MISHRA; Arunava SEN |
| Abstract: | We show that every cardinal incentive compatible voting mechanism satisfying a continuity condition, must be ordinal. Our results apply to many standard models in mechanism design without transfers, including the standard voting models with any domain restrictions. |
| Keywords: | incentive compatibility, cardinal utilities, ordinal |
| JEL: | D78 D82 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:04-2016&r=gth |
| By: | EHLERS, Lars; MAJUMDAR, Dipjyoti; MISHRA, Debasis; SEN, Arunava |
| Abstract: | We show that every cardinal incentive compatible voting mechanism satisfying a continuity condition, must be ordinal. Our results apply to many standard models in mechanism design without transfers, including the standard voting models with any domain restrictions. |
| Keywords: | Incentive compatibility; cardinal utilities; ordinal |
| JEL: | D78 D82 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2016-04&r=gth |