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on Game Theory |
| By: | Marina Núnez (Department of Mathematical Economics, Finance and Actuarial Sciences, University of Barcelona); Tamás Solymosi (‘Momentum’ Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences) |
| Abstract: | We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationships between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationships. Our main result is the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game. |
| Keywords: | Assignment game, extreme core payoff, Alexia value |
| JEL: | C71 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1425&r=gth |
| By: | Emiliya Lazarova (University of East Anglia, United Kingdom); Peter Borm (Tilburg University, the Netherlands); Arantza Est�vez-Fern�ndez (VU University Amsterdam, the Netherlands) |
| Abstract: | In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractually exchange stability and matchings of maximum total reward by means of compensation exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in the sense that there will be no subset of agents who can all by deviation obtain a higher reward. The proof of this result uses the fact that the core of an associated compensation matching game with constraints is nonempty. |
| Keywords: | matching, Pareto optimal matching, contractually exchange stability, compensation stability, compensation schedule |
| JEL: | C78 C71 D60 |
| Date: | 2014–07–08 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140086&r=gth |
| By: | Brams, Steven; Kilgour, D. Marc; Klamler, Christian |
| Abstract: | We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or Borda maximin—maximize the minimum rank, or the Borda score—of the items received by a player. Although SA is potentially vulnerable to manipulation, it would be difficult to manipulate in the absence of one player’s having complete information about the other players’ preferences. We discuss the applicability of SA, such as in assigning people to committees or allocating marital property in a divorce. |
| Keywords: | Fair division; indivisible items; envy-freeness |
| JEL: | C72 C78 D6 D61 D63 D7 D74 |
| Date: | 2014–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58370&r=gth |
| By: | Gilles Grandjean; Marco Mantovani; Ana Mauleon; Vincent Vannetelbosch |
| Abstract: | The paper analyzes the role of the structure of communication - i.e. who is talking with whom - on the choice of messages, on their credibility and on actual play. We run an experiment in a three-player coordination game with Pareto ranked equilibria, where a pair of agents has a profitable joint deviation from the Pareto-dominant equilibrium. According to our analysis of credibility, the subjects should communicate and play the Pareto optimal equilibrium only when communication is public. When pairs of agents exchange messages privately, the players should play the Pareto dominated equilibrium and disregard communication. The experimental data conform to our predictions: the agents reach the Pareto-dominant equilibrium only when announcing to play it is credible. When private communication is allowed, lying is prevalent, and players converge to the Pareto-dominated equilibrium. Nevertheless, at the individual level, players’ beliefs and choices tend to react to messages even when these are non-credible. |
| Keywords: | cheap talk, coordination, coalitions, experiment |
| JEL: | C72 C91 D03 D83 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-064&r=gth |
| By: | Dávid Csercsik (Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Pázmány Péter Catholic University) |
| Abstract: | Local routing protocols in scale free networks have been extensively studied. In this paper we consider a wireless contextualization of this routing problem and analyze on the one hand how cooperation affects network efficiency, and on the other hand the stability of cooperation structures. Cooperation is interpreted as local exchange of topological information between cooperating agents, and the payoff of a certain node is defined based on its energy consumption during the routing process. We show that if the payoff of the nodes is the energy saving compared to the all-singleton case, basically coalitions are not stable. We introduce coalitional load balancing and net reward to enhance coalitional stability and thus the more efficient operation of the network. As in the proposed model cooperation strongly affects routing dynamics of the network, externalities will arise and the game is defined in a partition function form. |
| Keywords: | partition function form games, networks, local routing |
| JEL: | C71 L14 L96 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1413&r=gth |
| By: | Cy Maor; Eilon Solan |
| Abstract: | In repeated games, cooperation is possible in equilibrium only if players are sufficiently patient, and long-term gains from cooperation outweigh short-term gains from deviation. What happens if the players have incomplete information regarding each other's discount factors? In this paper we look at repeated games in which each player has incomplete information regarding the other player's discount factor, and ask when full cooperation can arise in equilibrium. We provide necessary and sufficient conditions that allow full cooperation in equilibrium that is composed of grim trigger strategies, and characterize the states of the world in which full cooperation occurs. We then ask whether these "cooperation events" are close to those in the complete information case, when the information on the other player's discount factor is "almost" complete. |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1411.1368&r=gth |
| By: | De, Parikshit |
| Abstract: | In this paper we analyze the implication of a particular kind of allocation rule called Rawlsian allocation rule on queueing and sequencing problems. We find that in case of queueing problems, Efficient allocation rules are Rawlsian but the converse is not true. For a particular class of Rawlsian allocation rule we characterize the unique class of transfer rule that ensures non-manipulability. Also in case of a situation where there is private information in multiple dimension, we find that a the particular kind of Rawlsian allocation rule equipped with a suitable transfer rule works as a panacea. |
| Keywords: | Queueing problems, Sequencing problems, Strategyproofness, Rawlsian allocation. |
| JEL: | C72 D82 |
| Date: | 2014–07–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58744&r=gth |
| By: | Yoshitaka Okano (Kochi University of Technology) |
| Abstract: | Palacios-Huerta and Volij (2008) found that the behavior of professional soccer players in two-person zero-sum games is consistent with minimax play, while Wooders (2010) reexamined their data and found inconsistencies in several respects. This study applies a similar analysis of Wooders (2010) to the experimental data in Okano (2013), which found that the behavior of teams of two student subjects conforms closely to minimax play, and addresses whether teams exhibit the same inconsistencies as professionals. Teams were found to have consistency with minimax play, with no tendencies similar to those of professionals. |
| Keywords: | Experimental game, teams' decision making, minimax, zero-sum |
| JEL: | C72 C92 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2014-12&r=gth |
| By: | Thanh Nguyen (Krannert School of Management, Purdue University); Rakesh Vohra (Department of Economics, University of Pennsylvania) |
| Abstract: | The National Resident Matching program strives for a stable matching of medical students to teaching hospitals. With the presence of couples, stable matchings need not exist. For any student preferences, we show that each instance of a stable matching problem has a ’nearby’ instance with a table matching. The nearby instance is obtained by perturbing the capacities of the hospitals. Specifically, given a reported capacity for each hospital h, we find a redistribution of the slot capacities k¹h satisfying [kh –k¹h] ≤ 4 for all hospital h, and ∑h kh ≤ ∑ k¹h ≤ ∑h kh + 9, such that a stable matching exists with respect to k¹. Our approach is general and applies to other type of complementarities, as well as matchings with side constraints and contracts. |
| Keywords: | stable matching, complementarities, Scarf's lemma |
| JEL: | C78 |
| Date: | 2014–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:14-028&r=gth |
| By: | Chen, Heng; Luo, Yulei; Pei, Guangyu |
| Abstract: | This paper examines the welfare properties of “beauty contest†games with rationally inattentive agents. Agents allocate attention between private and public signals to reduce the uncertainty about observation noises. In this setting, social welfare may not necessarily increase with the capacity to process information, and can actually decrease as a result of attention misallocation. Strikingly, social welfare can be even higher when agents possess a finite amount of capacity than when they have an infinite amount of capacity. We derive sufficient and necessary conditions under which multiple equilibria emerge and study the implications of equilibrium multiplicity for macroeconomic policies. |
| Keywords: | Coordination game, social welfare, rational inattention |
| JEL: | C72 D60 E58 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59139&r=gth |
| By: | Daan in 't Veld (University of Amsterdam); Marco van der Leij (University of Amsterdam, and De Nederlandsche Bank, the Netherlands); Cars Hommes (University of Amsterdam, the Netherlands) |
| Abstract: | Recent empirical evidence suggests that financial networks exhibit a core periphery network structure. This paper aims at giving an economic explanation for the emergence of such a structure using network formation theory. Focusing on intermediation benefits, we find that a core periphery network cannot be unilaterally stable when agents are homogeneous. The best-response dynamics converge to a unique unilaterally stable outcome ranging from an empty to denser networks as the costs of linking decrease. A core periphery network structure can form endogenously, however, if we allow for heterogeneity among agents in size. We show that our model can reproduce the observed core periphery structure in the Dutch interbank market for reasonable parameter values. |
| Keywords: | financial networks, core periphery structure, network formation models |
| JEL: | D85 G21 L14 |
| Date: | 2014–07–28 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140098&r=gth |
| By: | Fischer, Sven; Guth, Werner; Kaplan, Todd; Zultan, Roi |
| Abstract: | We study first- and second-price private value auctions with sequential bidding where second movers may discover the first movers bids. There is a unique equilibrium in the first-price auction and multiple equilibria in the second-price auction. Consequently, comparative statics across price rules are equivocal. We experimentally find that in the first-price auction, leaks benefit second movers but harm first movers and sellers. Low to medium probabilities of leak eliminate the usual revenue dominance of first-price over second-price auctions. With a high probability of a leak, second-price auctions generate higher revenue. |
| Keywords: | auctions, espionage, collusion, laboratory experiments |
| JEL: | C72 C91 D44 |
| Date: | 2014–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58940&r=gth |
| By: | Tatsuyoshi Saijo (School of Management, Kochi University of Technology) |
| Abstract: | I consider systems with voluntary contribution mechanisms (VCM) in a quasilinear environment, showing that they are not asymptotically stable under simultaneous difference equations, and are structurally unstable under simultaneous differential equations. However, a VCM system is stable in a Cobb–Douglas (CD) environment under simultaneous differential equations; it is also stable under simultaneous difference equations given conditions on the slope of best response functions and the number of players. Most of the parameters investigated in nonlinear experiments on the VCM so far have been on the boundaries between stability and instability, and there has been hardly any work on instability. Therefore, research on the private provision of public goods faces a new challenge in addition to free riding. |
| JEL: | C62 C72 C92 H41 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2014-3&r=gth |
| By: | Dóra Balog (Corvinus University of Budapest, Department of Finance); Tamás László Bátyi (University of California, Berkeley, Department of Economics); Péter Csóka (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Finance, Corvinus University of Budapest); Miklós Pintér (Corvinus University of Budapest, Department of Mathematics and MTA-BCE Lendület Strategic Interactions Research Group) |
| Abstract: | In finance risk capital allocation raises important questions both from theoretical and practical points of view. How to share risk of a portfolio among its subportfolios? How to reserve capital in order to hedge existing risk and how to assign this to different business units? We use an axiomatic approach to examine risk capital allocation, that is we call for fundamental properties of the methods. Our starting point is Csóka and Pintér (2011) who show by generalizing Young (1985)'s axiomatization of the Shapley value that the requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity are irreconcilable given that risk is quantified by a coherent measure of risk. In this paper we look at these requirements using analytic and simulations tools. We examine allocation methods used in practice and also ones which are theoretically interesting. Our main result is that the problem raised by Csóka and Pintér (2011) is indeed relevant in practical applications, that is it is not only a theoretical problem. We also believe that through the characterizations of the examined methods our paper can serve as a useful guide for practitioners. |
| Keywords: | Coherent Measures of Risk, Risk Capital Allocation, Shapley value, Core, Simulation |
| JEL: | C71 G10 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1417&r=gth |
| By: | Michael Naef; Alessandro Sontuoso (Philosophy, Politics and Economics, University of Pennsylvania) |
| Abstract: | A correlation between second-order beliefs and strategies – in social dilemmas – has been interpreted as evidence of guilt aversion (Charness and Dufwenberg [2006]). Ellingsen et al. [2010] hypothesize that such correlation might rather be due to consensus effects. Here we propose an additional explanation, conformity, which involves a similar belief-behavior correlation and we set out to tell these motivations apart by proposing a design such that: (i) we reduce the scope for guilt aversion by eliciting and transmitting beliefs about the behavior of other participants in the same role; (ii) we disentangle consensus from conformity by providing an exogenous variation in collective beliefs. The data show that consensus is present (and predominant) but is not the only force driving the belief-behavior correlation. In fact, we also observe “self-servingly conformist” behavior in that subjects choose to match their strategy to the transmitted information when it is in their interest to do so. |
| Keywords: | conformist preferences, consensus effects, guilt aversion, social norms, trust, experiment |
| JEL: | C72 C91 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:ppc:wpaper:0002&r=gth |
| By: | Massimo Morelli; In-Uck Park |
| Abstract: | In deciding whether to join a coalition or not, an agent must consider both i) the expected power of the coalition and ii) her position in the vertical structure within the coalition. We establish the existence of a positive relationship between the degree of inequality in remuneration across ranks within coalitions and the number of coalitions to be formed endogenously in stable systems. An inherent feature of such coalitions is that they are mixed and balanced, rather than segregated, in terms of members abilities. When the surplus of a coalition is assumed to be linear in its relative power conditional on its size, we also establish the existence of stable systems and characterise them fully: a system is stable if and only if all coalitions are of an ecient size and every agent is paid her marginal contribution. (JEL Codes: C71, D71) Keywords: Stable systems, Abilities, Hierarchy, Cyclic partition. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:528&r=gth |
| By: | Salvador Barberà; Alejandro Neme |
| Abstract: | We propose a notion of r-rationality, based on the idea that the choices of individuals are guided by a single preference order, but rather than always choosing the very best available alternative, agents are content with selecting one of the r-best. This proposal provides a purely ordinal and relative version of the classical idea of satisficing behavior. No level of satisfaction is exogenously fixed, agents are not full maximizers, but they follow a clear pattern of behavior whose consequences generate testable implications, which we fully characterize. The notion of r-rationalizability is further extended to individuals whose ordinal satisficing level may vary depending on the set of available alternatives: a similar characterization obtains. Since any choice function F is n-rationalizable, we can ask for the minimal r(F) for which F is r(F) rationalizable, and take that value as a measure of the agent's degree of rationality. We provide an algorithm to compute it for any given F. Special cases of ordinal relative satisficing behavior are shown to result from a variety of choice models proposed in the literature. Our notion allows for further flexibility, yet still provides precise restrictions on observable data. |
| Keywords: | choice, rationality, satisficing behavior, rationazability, preferences, choice functions |
| JEL: | D71 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:790&r=gth |
| By: | Robert Burguet; Martin K. Perry |
| Abstract: | This paper examines preference in procurement with asymmetric suppliers. The preferred supplier has a right-of-first-refusal to obtain the contract at a price equal to the bid of a competing supplier. Despite the inefficiency created by the right-of-first-refusal, preference increases the joint surplus of the buyer and the preferred supplier. The buyer can increase his surplus by holding a pre-auction for the right-of-first-refusal. This is true even when the ex ante stronger supplier wins this pre-auction for preference. |
| Keywords: | procurement auctions, vertical integration, bargaining solutions |
| JEL: | D44 D82 C79 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:791&r=gth |
| By: | Oliver Kley; Claudia Kluppelberg; Gesine Reinert |
| Abstract: | We model business relationships exemplified for a (re)insurance market by a bipartite graph which determines the sharing of severe losses. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional Tail Expectation. We show that the dependence on the network structure plays a fundamental role in their asymptotic behaviour. As is well-known, if the Pareto exponent is larger than 1, then for the individual agent (re-insurance company) diversification is beneficial, whereas when it is less than 1, concentration on a few objects is the better strategy. The situation changes, however, when systemic risk comes into play. The random network structure has a strong influence on diversification effects, which destroys this simple individual agent's diversification rule. It turns out that diversification is always beneficial from a macro-prudential point of view creating a conflicting situation between the incentives of individual agents and the interest of some superior entity to keep overall risk small. We explain the influence of the network structure on diversification effects in different network scenarios. |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1410.8671&r=gth |