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on Game Theory |
| By: | Alex Possajennikov (School of Economics, University of Nottingham) |
| Abstract: | In a semi-aggregative representation of a game, the payoff of a player depends on a player's own strategy and on a personalized aggregate of all players' strategies. Suppose that each player has a conjecture about the reaction of the personalized aggregate to a change in the player's own strategy. The players play an equilibrium given their conjectures, and evolution selects conjectures that lead to a higher payoff in such an equilibrium. Considering one player role, I show that for any conjectures of the other players, only conjectures that are consistent can be evolutionarily stable, where consistency means that the conjecture is, to a first approximation, correct at equilibrium. I illustrate this result in public good games and contests. |
| Keywords: | semi-aggregative games, conjectural variations, evolutionary stability, public good games, contests |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2016-08&r=gth |
| By: | Nicola, Gatti; Mario, Gilli; Fabio, Panozzo |
| Abstract: | The computational study of games is receiving increasing attention both in game theory and computer science. The challenge is distinguishing computationally tractable problems (also said easy), admitting polynomial{time algorithms, from the intractable ones (also said hard). In this paper, we focus on extensive form games, as the computational problems defined on such games are largely unexplored. We study the problem (aka verification problem) of certifying that a solution given in input is an equilibrium according to different refinements for extensive form games as the input change. We show that, when the input is a realization plan strategy profile (i.e., strategies for the sequence form representation), deciding whether the input is a Subgame Perfect Equilibrium or is a part of a Sequential Equilibrium is NP-hard even in two-player games (we conjecture the same holds also for Quasi Perfect Equilibrium). This means that there is no polynomial-time algorithm unless P = NP, but it is commonly believed that P x NP. Subsequently, we show that in two{player games, when the input is a behavioral strategy profile, there is a polynomial-time algorithm deciding whether the input is a Quasi-Perfect Equilib- rium, and a simple variation of the algorithm decides whether the input is part of some Sequential Equilibrium (in games with three or more players, the problem is known to be NP{hard for both Quasi-Perfect Equilibrium and Sequential Equilibrium). Finally, we show that, when the input is an assessment, there is a polynomial{time algorithm deciding whether the input is a Sequential Equilibrium regardless the number of players. |
| Keywords: | Ecient algorithms, extensive{form re nements |
| JEL: | C7 |
| Date: | 2016–07–15 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:347&r=gth |
| By: | Puppe, Clemens; Slinko, Arkadii |
| Abstract: | Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it contains the majority relation of every profile with an odd number of voters whose preferences belong to this domain. We show that every closed Condorcet domain can be endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (in general, not uniquely). Condorcet domains that have linear graphs (chains) associated with them are exactly the preference domains with the classical single-crossing property. As a corollary, we obtain that a domain with the so-called 'representative voter property' is either a single-crossing domain or a very special domain containing exactly four different preference orders whose associated median graph is a 4-cycle. Maximality of a Condorcet domain imposes additional restrictions on the associated median graph. We prove that among all trees only (some) chains can be associated graphs of maximal Condorcet domains, and we characterize those single-crossing domains which are maximal Condorcet domains. Finally, using the characterization of Nehring and Puppe [2007] of monotone Arrovian aggregation, our analysis yields a rich class of strategy-proof social choice functions on any closed Condorcet domain. |
| Keywords: | social choice,Condorcet domains,acyclic sets of linear orders,median graphs,single-crossing property,distributive lattice,Arrovian aggregation,strategy-proofness,intermediate preferences |
| JEL: | D71 C72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:92&r=gth |
| By: | Andersson, Tommy (Department of Economics, Lund University); Ehlers , Lars (Département de sciences économiques and CIREQ, Université de Montréal) |
| Abstract: | In Sweden, asylum seekers are either deported or granted a residence permit. Refugee families with a residence permit are assigned to the different local municipalities. Since almost all accommodation options are exhausted in Sweden, households in some municipalities are asked to state their willingness to accommodate refugee families. In line with the European NGO “Refugees Welcome”, a refugee family and a landlord (household) are mutually acceptable if they have a language in common and if the number of offered beds of the household exceeds the number of beds needed by the refugee family. This paper proposes an algorithm that finds a maximum matching (filling the maximal number of beds) which in addition is stable. |
| Keywords: | Refugees; landlords; stability; maximum matchings; market design |
| JEL: | C71 C78 D71 D78 |
| Date: | 2016–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2016_018&r=gth |
| By: | Sofia Moroni |
| Abstract: | In revision games a group of players can move at stochastic opportunities before adeadline. Their payoffs are determined by the sequence of actions taken before the endof the game. In this paper I define trembling hand equilibrium in a large class of revisiongames that may feature incomplete and imperfect information, and show that tremblinghand equilibria exist. Since trembling hand perfect equilibria are also Nash, existence ofa Nash equilibrium follows. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:pit:wpaper:5874&r=gth |
| By: | Igor V. EVSTIGNEEV (University of Manchester); Thorsten HENS (University of Zürich and Swiss Finance Institute); Klaus Reiner SCHENK-HOPPÉ (University of Manchester) |
| Abstract: | The paper reviews a new research field that develops evolutionary and behavioural approaches for the modeling of financial markets. The main objective is to create a plausible alternative to the conventional Walrasian equilibrium theory based on the hypothesis of full rationality of market players. Rather than maximizing typically unobservable individual utility functions, traders/investors are permitted to have a whole variety of patterns of strategic behaviour depending on their individual psychology. The models considered in this field combine elements of evolutionary game theory (solution concepts) and stochastic dynamic games (strategic frameworks). |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1516&r=gth |
| By: | Bettina Klaus; Panos Protopapas |
| Abstract: | We consider the problem of choosing a set of locations of a public good on the real line. Similarly to Klaus and Storcken (2002), we ordinally extend the agents' preferences over compact subsets of the real line, and extend the results of Ching and Thomson (1996), Vohra (1909), and Klaus (2001) to choice correspondences. Specifically, we show that Pareto-efficiency and either population-monotonicity or one-sided replacement-domination characterize the class of target set correspondences on the domains of single-peaked preferences and symmetric single-peaked preferences. |
| Keywords: | choice correspondences; Pareto-eciency; population-monotonicity; replacement-domination; single-peaked preferences; solidarity |
| JEL: | C71 D63 D78 H41 |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:16.14&r=gth |
| By: | Luca Rigotti |
| Abstract: | We provide evidence on how cooperation rates vary across payoff parameters in the Prisoner’s Dilemma (PD), using four one-shot games that differ only in the payoffs from mutual cooperation. In our experiment, participants play only the PD game, and play the game once and only once, so there are no potential confounds or methodological issues. Our results show that higher monetary payoffs from cooperation are associated with substantially higher cooperation rates, which increase monotonically from 23% to 60%. Participants’ beliefs about cooperation rates track closely actual cooperation rates: higher cooperation is expected from others when mutual cooperation payoffs are higher. This is true also for participants who, in a follow-up experiment, only make guesses about the choices of others. |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:pit:wpaper:5877&r=gth |
| By: | Lu Dong (School of Economics, University of Nottingham); Rod Falvey (Bond Business School, Bond University); Shravan Luckraz (School of Economics, University of Nottingham, Ningbo China) |
| Abstract: | We propose and experimentally test a mechanism for a class of principal-agent problems in which agents can observe each others' efforts. In this mechanism each player costlessly assigns a share of the pie to each of the other players, after observing their contributions, and the final distribution is determined by these assignments. We show that cooperation can be achieved under this simple mechanism and, in a controlled laboratory experiment, we find that players use a proportional rule to reward others in most cases and that the players' contributions improve substantially and almost immediately with 80% of players contributing fully. |
| Keywords: | mechanism design, experimental economics, fairness, distributive justice |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2016-10&r=gth |
| By: | Alexander Rubchinsky |
| Abstract: | In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor) divisions, unlikely the case where all the items are divisible, not always exist. The necessary and sufficient conditions of existence of proportional and equitable division were found. |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1607.02423&r=gth |
| By: | Francesco Nava |
| Abstract: | The paper analyzes quantity competition in economies in which a network describes the set of feasible trades. A model is presented in which the identity of buyers, of sellers, and of intermediaries is endogenously determined by the trade flows in the economy. The analysis first considers small economies, and provides sufficient conditions for equilibrium existence, a characterization of prices and flows, and some negative results relating welfare to network structure. The second and central part of the analysis considers behavior in large markets, and presents necessary and sufficient conditions on the network structure for equilibria to be approximately efficient when the number of players is large. |
| Keywords: | decentralized markets; intermediation; oligopoly; efficiency; market power |
| JEL: | C7 D6 D85 L13 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:61879&r=gth |
| By: | Morone, Andrea; Nuzzo, Simone; Caferra, Rocco |
| Abstract: | By means of a laboratory experiment, this paper aims at studying how individuals and groups behave in a simple game such as the dollar auction. This game is extremely interesting since it induces subjects to fall prey into the paradigm of escalation, which is driven by agents’ commitment to higher and higher bids. Indeed, whenever each participant commits himself to a bid, the lower bidder, moved by the wish to win as well as to defend his prior investment, finds it in his best interest to place a higher bid to overcome his opponent. The latter mechanism may lead subjects to overbid, implying that the winner pays more than the auctioned value. The aim of the paper is to analyze bidder’s behavior, comparing individuals vs. groups’ decisions within the dollar auction framework. We find that groups are closer than individuals to the Nash equilibrium, and that experience reduces the escalation phenomenon, but it has a different impact on winners and losers. |
| Keywords: | escalation; winner’s curse |
| JEL: | C91 |
| Date: | 2016–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:72608&r=gth |
| By: | Romulus Breban |
| Abstract: | We consider a large community of individuals who mix strongly and meet in pairs to bet on a coin toss. We investigate the asset distribution of the players involved in this zero-sum repeated game. Our main result is that the asset distribution converges to the exponential distribution, irrespective of the size of the bet, as long as players can never go bankrupt. Analytical results suggests that the exponential distribution is a stable fixed point for this zero-sum repreated game. This is confirmed in numerical experiments. |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1607.03161&r=gth |
| By: | Colasante, Annarita |
| Abstract: | This paper presents an investigation about cooperation in a Public Good Game using an Agent Based Model calibrated on experimental data. Starting from the experiment proposed in Colasante and Russo (2016), we analyze the dynamic of cooperation in a Public Good Game where agents receive an heterogeneous income and choose both the level of contribution and the distribution rule. The starting point is the calibration and the output validation of the model using the experimental results. Once tested the goodness of fit of the Agent Based Model, we run some policy experiment in order to verify how each distribution rule, i.e. equidistribution, proportional to contribution and progressive, affects the level of contribution in the simulated model. We find out that the share of cooperators decreases over time if we exogenously set the equidistribution rule. On the contrary, the share of cooperators converges to 100% if we impose the progressive rule. Finally, the most interesting result refers to the effect of the progressive rule. We observe that, in the case of high inequality, this rule is not able to reduce the heterogeneity of income. |
| Keywords: | Public Good Game, Cooperation, Social Influence |
| JEL: | C63 D71 H41 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:72577&r=gth |
| By: | Dominik Karos |
| Abstract: | The members of a society are faced with the decision whether or not to participate in an anti-government protest. Their utilities depend on their own decision but also on those of their neighbors in an underlying social network. They randomly observe other people's decisions, gather information on who is already active, and base their decision on their information. The model uses a Markov process (that depends on the underlying social network) to analyze who will become active over time. Two new features are essential: first, only very mild assumptions about the underlying social network are made, in particular agents can be entirely heterogeneous. Second, individuals are allowed to coordinate their decision if they mutually observe each other. The government can use political violence in order to change people's utility from being active. The probability of a revolution can thereby be reduced in the short run, but not in the long run. Under political repression protests do not increase gradually, but suddenly; and the conditional probability of a quick revolution given a protest increases if the regime turns violently against the protesters. Since large jumps in the number of activists depend on their capability to coordinate, the repression of political activism is more effective in countries where social media are not easily accessible. The findings are illustrated by data on the number of protests and revolutions world-wide depending on a country's number on the Political Terror Scale. |
| Keywords: | Social Networks, Coordination, Strong Nash Equilibrium, Innovation Diffusion, Unanticipated Revolutions, Political Repression |
| JEL: | C72 D85 O33 |
| Date: | 2016–07–06 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:797&r=gth |
| By: | Pauline Rossi (Paris-Jourdan Sciences Économiques (PSE) Paris School of Economics) |
| Abstract: | This paper proposes a strategic framework to account for fertility choices in polygamous households. A theoretical model specifies the main drivers of fertility in the African context and describes how the fertility of one wife might impact the behavior of her co-wives. It generates predictions to test for strategic interactions. Exploiting original data from a household survey and the Demographic and Health Surveys in Senegal, empirical tests show that children are strategic complements. One wife raises her fertility in response to an increase by the other wife, because children are the best claim to resources controlled by the husband. This result is the first quantitative evidence of a reproductive rivalry between co-wives. It suggests that the sustained high level of fertility in Africa does not merely reflect women's lack of control over births, as is often argued, but also their incentives to have many children. This paper also contributes to the literature on household behavior as one of the few attempts to open the black box of non-nuclear families. |
| Keywords: | Fertility, Polygamy, Africa, Noncooperative models, Duration models |
| JEL: | C72 D13 J13 J16 O15 O55 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:duh:wpaper:1601&r=gth |
| By: | Luca Anderlini (Georgetown University); Leonardo Felli (London School of Economics); Giovanni Immordino (Università di Napoli Federico II and CSEF) |
| Abstract: | Legal disputes are either settled or end up in Court. Settling a dispute involves some costs (time and money invested in preparations) that the parties have to incur ex-ante, in order for the pretrial negotiation and possible agreement to become feasible. Even in a full information world, if the distribution of these costs is sufficiently mismatched with the distribution of the parties' bargaining powers, a pretrial agreement may never be reached even though actual Court litigation is overall wasteful. As parameters vary, the equilibrium of our full information model with costly pretrial agreements sheds light on two key features of how disputes are initiated and subsequently handled. First, in some cases a Plaintiff may initiate a law suit even though the parties fully anticipate that it will be settled out of Court. Second, the “likelihood” that a given law suit ends up in Court is unaffected by the way trial costs are distributed among the litigants (e.g. English Rule or American Rule). The choice of fee-shifting rule can only affect whether the Plaintiff files a law suit in the first place. It does not affect whether a given suit is settled before trial or litigated in Court. |
| Keywords: | Pretrial Agreements, Costly Negotiations, Court Litigation |
| JEL: | D23 D86 C79 K12 K13 |
| Date: | 2016–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:449&r=gth |