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on Game Theory |
| By: | Sam Ganzfried; Austin Nowak; Joannier Pinales |
| Abstract: | Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a 3-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all. |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1804.04789&r=gth |
| By: | Nicola, Gatti; Mario, Gilli; Alberto, Marchesi; |
| Abstract: | Van Damme [1984] introduces the concept of quasi-perfect equilibrium, which refines sequential equilibrium as well as normal-form perfect equilibrium. It has been argued by Mertens [1995] that quasi-perfection is conceptually superior to extensive- form perfection, since quasi-perfection guarantees normal-form perfection, which for two-player games is equivalent to admissibility. On the other hand, while extensive-form perfect equilibria are defined as limit points of sequences of Nash equilibria of a general class of perturbed games in extensive form, till now, to the best of our knowledge, there is no characterization of quasi-perfect equilibria in terms of limit points of equilibria of perturbed games. The only known result is Lemma 1 by Miltersen and Sorensen [2010], showing that limit points of sequences of Nash equilibria of a particular class of perturbed games in sequence form are quasi-perfect equilibria of the original, unperturbed game in extensive form. However, as the authors point out, their main result only proves that a subset of the quasi-perfect equilibria can be obtained as limit points of equilibria of their class of perturbed games, and, thus, their paper provides no characterization of quasi-perfect equilibria in terms of perturbed games. The present paper fills this gap providing such characterization, showing that any quasi-perfect equilibrium can be obtained as limit point of a sequence of Nash equilibria of a certain class of perturbed games in sequence form, at least for the case of two-player games with nature. This result shows that the sequence form is not merely a computationally efficient representation, but it also captures game features that other forms are not able to effectively express. |
| Keywords: | Non-cooperative Game Theory, Extensive Games, Nash Equilibrium Refinements |
| JEL: | C70 C72 |
| Date: | 2018–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:389&r=gth |
| By: | Björn Brügemann (Department of Economics, Vrije Universiteit Amsterdam); Pieter Gautier (Department of Economics,Vrije Universiteit Amsterdam); Guido Menzio (Department of Economics, University of Pennsylvania) |
| Abstract: | We study two wage bargaining games between a Â…rm and multiple workers. We revisit the bargaining game proposed by Stole and Zwiebel (1996a). We show that, in the unique Subgame Perfect Equilibrium, the gains from trade captured by workers who bargain earlier with the firm are larger than those captured by workers who bargain later, as well as larger than those captured by the firm. The resulting equilibrium payffs are different from those reported in Stole and Zwiebel (1996a) as they are not the Shapley values. We propose a novel bargaining game, the Rolodex game, which follows a simple and realistic protocol. In the unique no-delay Subgame Perfect Equilibrium of this game, the payoffs to the firm and to the workers are their Shapley values. |
| Keywords: | Intra Örm bargaining; Shapley value |
| JEL: | D21 J30 |
| Date: | 2018–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:18-003&r=gth |
| By: | Moldovanu, Benny |
| Abstract: | We study the revenue maximizing allocation of m units among n symmetric agents that have unit demand and convex preferences over the probability of receiving an object. Such preferences are naturally induced by a game where the agents take costly actions that affect their values before participating in the mechanism. Both the uniform m + 1 price auction and the discriminatory pay-your-bid auction with reserve prices constitute symmetric revenue maximizing mechanisms. Contrasting the case with linear preferences, the optimal reserve price reacts to both demand and supply, i.e., it depends both on the number of objects m and on number of agents n. The main tool in our analysis is an integral inequality involving majorization, super-modularity and convexity due to Fan and Lorentz (1954). |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13259&r=gth |
| By: | Shuige Liu |
| Abstract: | We characterize three interrelated concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model for a game with incomplete information. Based on it, we give two groups of characterizations. The first group characterizes permissibility and proper rationalizability. The second group characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are two (compatible) refinements of permissibility within the complete information framework. The intrinsic difference between the two groups are the role of rationality: the first group does not need it, while the second group does. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.01933&r=gth |
| By: | Joseph Abdou (Centre d'Economie de la Sorbonne); Hans Keiding (University of Copenhagen - Department of Economics) |
| Abstract: | We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex |
| Keywords: | Delegation; compromise; simplicial complex; contiguity; strong homotopy |
| JEL: | C70 C79 |
| Date: | 2018–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:18033&r=gth |
| By: | Jeannette Brosig-Koch; Timo Heinrich; Heike Hennig-Schmidt; Claudia Keser; Joachim Weimann |
| Abstract: | Since Mancur Olson's "Logic of collective action" it is common conviction in social sciences that in large groups the prospects of a successful organization of collective actions are rather bad. Following Olson’s logic, the impact of an individual’s costly contribution becomes smaller if the group gets larger and, consequently, the incentive to cooperate decreases with group size. Conducting a series of laboratory experiments with large groups of up to 100 subjects, we demonstrate that Olson's logic does not generally account for observed behavior. Large groups in which the impact of an individual contribution is almost negligible are still able to provide a public good in the same way as small groups in which the impact of an individual contribution is much higher. Nevertheless, we find that small variations of the MPCR in large groups have a strong effect on contributions. We develop a hypothesis concerning the interplay of MPCR and group size, which is based on the assumption that the salience of the advantages of mutual cooperation plays a decisive role. This hypothesis is successfully tested in a second series of experiments. Our result raises hopes that the chance to organize collective action of large groups is much higher than expected so far. Since Mancur Olson's "Logic of collective action" it is common conviction in social sciences that in large groups the prospects of a successful organization of collective actions are rather bad. Following Olson’s logic, the impact of an individual’s costly contribution becomes smaller if the group gets larger and, consequently, the incentive to cooperate decreases with group size. Conducting a series of laboratory experiments with large groups of up to 100 subjects, we demonstrate that Olson's logic does not generally account for observed behavior. Large groups in which the impact of an individual contribution is almost negligible are still able to provide a public good in the same way as small groups in which the impact of an individual contribution is much higher. Nevertheless, we find that small variations of the MPCR in large groups have a strong effect on contributions. We develop a hypothesis concerning the interplay of MPCR and group size, which is based on the assumption that the salience of the advantages of mutual cooperation plays a decisive role. This hypothesis is successfully tested in a second series of experiments. Our result raises hopes that the chance to organize collective action of large groups is much higher than expected so far. |
| Date: | 2018–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2018s-02&r=gth |
| By: | Claudia Keser; Stephan Müller; Emmanuel Peterlé; Holger A. Rau |
| Abstract: | This paper experimentally tests the relation between subjects’ competitiveness and bargaining behavior. Bargaining is investigated in a demand-ultimatum game, where the responder can request a share of the pie from the proposer. The re-sults show that highly competitive proposers earn less, since they make lower offers, which are more often rejected. Similarly, highly competitive responders achieve lower payoffs, since they request excessive amounts which induces lower proposals. These findings establish a link between competitiveness and bargaining as suggested by social and evolutionary psychology. Thus, we identify one driver of the empirical heterogeneity of bargaining behavior and outcomes. From a management perspec-tive our findings highlight that giving thought to employees’ competitiveness before delegating them to participate in negotiations may pay off. |
| Keywords: | Bargaining,Competitiveness,Experiment, |
| JEL: | C91 M54 |
| Date: | 2018–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2018s-08&r=gth |
| By: | Qinxin Guo (Graduate School of Economics, Kobe University, Japan); Enci Wang (School of Economics, Shanghai University, China); Yongyou Nie (School of Economics, Shanghai University, China); Junyi Shen (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan) |
| Abstract: | In this study, we implemented a dictator game experiment to examine how the increase of the public characteristic in an impure public good affects individuals’ prosocial behavior. A within-subject design was used in the experiment. The dictator game was repeated six times with an impure public good introduced in four of them. We observe that the increase of the public characteristic in an impure public good partly crowds out individuals’ subsequent donations, which could be explained by a seemingly “mental accounting” mental process. In addition, we also find that the selfish behavior of individuals in dictator games with impure public goods, to some extent, has an inertia influence on their subsequent donations when the impure public good is removed. |
| Keywords: | Impure public goods, Dictator game, Multiple dictators, Mental accounting |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2018-22&r=gth |
| By: | Rigos, Alexandros (Department of Economics, Lund University) |
| Abstract: | This paper studies how large populations of rationally inattentive individuals acquire and use information about economic fundamentals when, along with the motive to accurately estimate the fundamental, they are driven by coordination motives. Information acquisition is costly but flexible: players design their information channel by determining the distribution of the signal that they receive and arbitrarily correlating it with the fundamental. Costs are linear in the reduction of Shannon entropy. Firstly, the classes of equilibria in which players use continuous strategies and equilibria without information acquisition are characterized. This is achieved without assuming a normal prior for the fundamental. Secondly, equilibria where the population-wide average action is an affine function of the fundamental exist only when the fundamental is normally distributed. This indicates that equilibrium tractability heavily depends on the normality assumption prevalent in existing literature. Finally, multiple equilibria occur under some parameter regions with high coordination motiv |
| Keywords: | Coordination games; Beauty-contest; Flexible information acquisition; Rational inattention; Non-normal prior |
| JEL: | C72 D83 |
| Date: | 2018–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2018_030&r=gth |
| By: | Glazer, Jacob; Herrera, Helios; Perry, Motty |
| Abstract: | We propose a model of product reviews with honest and fake reviews to study the value of information provided on platforms like TripAdvisor, Yelp, etc. In every period, a review is posted which is either honest, namely reveals the reviewer's true experience with the product/service, or fake, namely entirely fabricated in order to manipulate the public's beliefs. We establish that the equilibrium is unique and derive robust and interesting results about these markets. While fake agents are able to affect the public's beliefs in their preferred direction, aggregation of information takes place as long as some of the reviews are honest. |
| Keywords: | Sender-Receiver Games |
| JEL: | C72 D82 D83 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13244&r=gth |
| By: | Guillaume Rocheteau (Department of Economics, University of California-Irvine); Lucie Lebeau (Department of Economics, University of California-Irvine); Tai-Wei Hu (University of Bristol); Younghwan In (KAIST College of Business) |
| Abstract: | We introduce a new approach to bargaining, with strategic and axiomatic foundations, into models of decentralized asset markets. Bargaining with an agenda assumes that asset portfolios are partitioned into bundles sold sequentially, and encompasses both the Nash and Kalai solutions as special cases. Gradual negotiations are optimal for portfolio holders and, in general equilibrium, they raise social welfare by reducing asset misallocation. In the presence of multiple assets, our theory generates a pecking order, and di§erences in returns and turnover. We apply our model to the study of open-market operations and the determination of the exchange rate between (crypto-)currencies. |
| Keywords: | Decentralized asset markets; Bargaining with an agenda; Nash program; Rate-of-return dominance |
| JEL: | D83 |
| Date: | 2018–09 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:181904&r=gth |
| By: | Moldovanu, Benny |
| Abstract: | Agents in a finite two-sided market are matched assortatively, based on costly investments. Besides signaling privately known, complementary types, the investments also directly benefit the match partner. The bilateral external benefits induce a complex feedback cycle that amplifies the agents' signaling investments. Our main results quantify how the feedback effect depends on the numbers of competitors on both sides of the market. This yields detailed insights into the equilibria of two-sided matching contests with incomplete information, in particular for markets of small or intermediate size. It also allows us to shed some new light on the relationship between finite and continuum models of pre-match investment. |
| Keywords: | feedback effect; investment; Matching; signaling |
| JEL: | C78 D44 D82 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13258&r=gth |
| By: | Dina Tasneem; Audrey Azerot; Marine de Montaignac; Jim Engle-Warnick |
| Abstract: | We report results from an on-line economics experiment that examines the effect of nudging retirement savings decisions. In the experiments, participants make decisions in a finitely repeated retirement savings game, in which income during working years is uncertain, and retire-ment age is known. Participants, who are household financial decision-makers, are nudged with automatic savings in each period of the game. We find that that the nudge simply replaced nat-ural decision-making observed in the absence of a nudge in this experiment, even to the extent that it resulted in nearly identical inferred decision rules. This surprising result highlights the unpredictability of the effect of nudging human behavior. |
| Keywords: | Precautionary Savings,Retirement Savings,Life-cycle Models,Dynamic Optimization,Decision Heuristics,Nudge,Choice Architecture, |
| JEL: | C91 E21 C61 |
| Date: | 2018–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2018s-23&r=gth |
| By: | Aislinn Bohren (Department of Economics, University of Pennsylvania) |
| Abstract: | I study how the persistence of past choices can be used to create incentives in a continuous time stochastic game in which a large player, such as a ï¬ rm, interacts with a sequence of short-run players, such as customers. The long-run player faces moral hazard and her past actions are imperfectly observed – they are distorted by a Brownian motion. Persistence refers to the fact that actions impact a payoffrelevant state variable, e.g. the quality of a product depends on both current and past investment choices. I obtain a characterization of actions and payoffs in Markov Perfect Equilibria (MPE), for a ï¬ xed discount rate. I show that the perfect public equilibrium (PPE) payoff set is the convex hull of the MPE payoff set. Finally, I derive sufficient conditions for a MPE to be the unique PPE. Persistence creates effective intertemporal incentives to overcome moral hazard in settings where traditional channels fail. Several applications illustrate how the structure of persistence impacts the strength of these incentives. |
| Keywords: | Continuous Time Games, Stochastic Games, Moral Hazard |
| JEL: | C73 L1 |
| Date: | 2018–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:18-015&r=gth |
| By: | Richard McLean (Department of Economics, Rutgers University); Andrew Postlewaite (Department of Economics, University of Pennsylvania) |
| Abstract: | A single unit of a good is to be sold by auction to one of many potential buyers. There are two equally likely states of the world. Potential buyers receive noisy signals of the state of the world. The accuracies of buyers ’signals may di¤er. A buyer’s valuation is the sum of a common value component that depends on the state and an idiosyncratic private value component independent of the state. The seller knows nothing about the accuracies of the signals or about buyers’ beliefs about the accuracies. It is common knowledge among buyers that the accuracies of the signals are conditionally independent and uniformly bounded below 1 and above 1=2, and nothing more. We demonstrate a modifi…ed second price auction that has the property that, for any " > 0; the seller’s expected revenue will be within " of the highest buyer expected value when the number of buyers is sufficiently large and buyers make undominated bids. |
| Date: | 2018–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:18-001&r=gth |
| By: | Dina Tasneem; Audrey Azerot; Marine de Montaignac; Jim Engle-Warnick |
| Abstract: | We report results from an economics experiment that examines the role of financial literacy in retirement savings. In the experiments, participants make decisions in a retirement savings game, in which income during working years is uncertain. Participants are nudged to varying degrees with automatic savings in each period of the game. Some participants receive financial literacy training in the form of training to compute the expected savings needed at retirement to smooth consumption over the entire life cycle. We find ev-idence that literacy increases savings and improves efficiency. Our finding has implications for choice architecture for retirement savings. |
| Keywords: | Precautionary Savings,Retirement Savings,Life-cycle Model,Dynamic Optimization,Nudge,Financial Literacy,Decision Heuristics, |
| JEL: | C90 |
| Date: | 2018–07–30 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2018s-24&r=gth |
| By: | Davillas, Apostolos; Jones, Andrew M. |
| Abstract: | We use a set of biomarkers to measure inequality of opportunity (IOp) in health in the UK. Applying a direct ex ante IOp approach, we find that inequalities in health attributed to circumstances account for a non-trivial part of the total health variation. For example, observed circumstances account for 20% of the total inequalities in our composite measure of multi-system health risk, allostatic load. Shapley decompositions show that apart from age and gender, education and childhood socioeconomic status are sources of IOp. We propose an extension to the decomposition of ex ante IOp to complement the mean-based approach, analysing the contribution of circumstances across the quantiles of the biomarker distributions. This shows that, for most of the biomarkers, the percentage contribution of socioeconomic circumstances, relative to differences attributable to age and gender, increases towards the right tail of the biomarker distribution, where health risks are more pronounced. |
| Date: | 2018–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:ese:iserwp:2018-13&r=gth |
| By: | Simon Jäger; Benjamin Schoefer; Samuel G. Young; Josef Zweimüller |
| Abstract: | Nonemployment is often posited as a worker's outside option in wage setting models such as bargaining and wage posting. The value of this state is therefore a fundamental determinant of wages and, in turn, labor supply and job creation. We measure the effect of changes in the value of nonemployment on wages in existing jobs and among job switchers. Our quasi-experimental variation in nonemployment values arises from four large reforms of unemployment insurance (UI) benefit levels in Austria. We document that wages are insensitive to UI benefit levels: point estimates imply a wage response of less than $0.01 per $1.00 UI benefit increase, and we can reject sensitivities larger than 0.03. In contrast, a calibrated Nash bargaining model predicts a sensitivity of 0.39 – more than ten times larger. The empirical insensitivity holds even among workers with a priori low bargaining power, with low labor force attachment, with high predicted unemployment duration, among job switchers and recently unemployed workers, in areas of high unemployment, in firms with flexible pay policies, and when considering firm-level bargaining. The insensitivity of wages to the nonemployment value we document presents a puzzle to widely used wage setting protocols, and implies that nonemployment may not constitute workers' relevant threat point. Our evidence supports wage-setting mechanisms that insulate wages from the value of nonemployment. |
| JEL: | D43 D83 E0 E2 E24 H0 H22 H55 J0 J2 J3 J30 J31 J41 J42 J5 J6 J64 J65 M5 M52 |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25230&r=gth |