
on Game Theory 
By:  Thomas Demuynck (Ecares, Université Libre de Bruxelles); JeanJacques Herings (Department of Economics, Maastricht University); Riccardo D. Saulle (Department of Economics, Maastricht University); Christian Seel (Department of Economics, Maastricht University) 
Abstract:  We introduce a new solution concept for models of coalition formation, called the myopic stable set. The myopic stable set is defined for a very general class of social environments and allows for an infinite state space. We show that the myopic stable set exists and is nonempty. Under minor continuity conditions, we also demonstrate uniqueness. Furthermore, the myopic stable set is a superset of the core and of the set of pure strategy Nash equilibria in noncooperative games. Additionally, the myopic stable set generalizes and unifies various results from more specific environments. In particular, the myopic stable set coincides with the coalition structure core in coalition function form games if the coalition structure core is nonempty; with the set of stable matchings in the standard onetoone matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in finite supermodular games, finite potential games, and aggregative games. We illustrate the versatility of our concept by characterizing the myopic stable set in a model of Bertrand competition with asymmetric costs, for which the literature so far has not been able to fully characterize the set of all (mixed) Nash equilibria. 
Keywords:  Social Environments, Group Formation, Stability, Nash Equilibrium 
JEL:  C70 C71 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2017.26&r=gth 
By:  Batabyal, Amitrajeet 
Abstract:  In this note we use a simple game model to analyze the optimal cleanup of an apartment that is shared by n ∈ ℕ college students who are pressed for time. From an individual standpoint, these students dislike cleaning. However, they also prefer a clean apartment to a dirty one. Hence, for any student i, where i=1,...,n, this student’s utility is the total number of hours spent by all the n students cleaning less a number d times the hours spent cleaning by himself. In this setting, we first determine the Nash equilibrium cleanup times when the number d is less than unity. Second, we find the Nash equilibrium cleanup times when d is greater than unity. Finally, for specific values of n and d, we investigate whether the second Nash equilibrium is Pareto efficient. 
Keywords:  Apartment, Cleanup, College Student, Nash Equilibrium, Static Game 
JEL:  C72 D01 J22 
Date:  2017–06–12 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:79887&r=gth 
By:  Dimitrios Xefteris; Nicholas Ziros 
Abstract:  We study twoparty elections considering that: a) prior to the voting stage voters are free to trade votes for money according to the rules of the ShapleyShubik strategic market games; and b) voters' preferences both ordinal rankings and cardinal intensities are public information. While under plurality rule no trade occurs, under a powersharing system (voters' utilities are proportionally increasing in the vote share of their favorite party) full trade is always an equilibrium (two voters the strongest supporter of each party buy the votes of all others). Notably, this equilibrium implements proportional justice with respect to the two buyers: the ratio of the parties' vote shares is equal to the ratio of the preference intensities of the two most opposing voters. 
Keywords:  Vote trading; Complete information; Strategic market games; Power sharing; Proportional justice. 
JEL:  C72 D72 P16 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:ucy:cypeua:032017&r=gth 
By:  Sonja Brangewitz (Paderborn University); Behnud Mir Djawadi (Paderborn University); Angelika Endres (Paderborn University); Britta Hoyer (Paderborn University) 
Abstract:  We experimentally study the emergence of networks under a known external threat. To be more specific, we deal with the question if subjects in the role of a strategic Designer are able to form safe and efficient networks while facing a strategic Adversary who is going to attack their networks. This investigation relates theoretical predictions by Dziubinski and Goyal (2013) to actual observed behaviour. Varying the costs for protecting nodes, we designed and tested two treatments with different predictions for the equilibrium network. Furthermore, the influence of the subjects' farsightedness on their decisionmaking process was elicited and analysed. We find that while subjects are able to build safe networks in both treatments, equilibrium networks are only built in one of the two treatments. In the other treatment, predominantly safe networks are built but they are not efficient. Additionally, we find that farsightedness as measured in our experiment has no influence on whether subjects are able to build safe or efficient networks. 
Keywords:  Networks Experiment, Network Design, Network Defence, Network Disruption 
JEL:  D03 D85 C91 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2017.30&r=gth 
By:  Sareh Vosooghi (University of Oxford) 
Abstract:  I examine a setting, where an information sender conducts research into a payoffrelevant state variable, and releases information to agents, who consider joining a coalition. The agents' actions can cause harm by contributing to a public bad. The sender, who has commitment power, by designing an information mechanism (a set of signals and a probability distribution over them), maximises his payoff, which depends on the action taken by the agents, and the state variable. I show that the coalition size, as a function of beliefs of agents, is an endogenous variable, induced by the information sender. The optimal information mechanism from the general set of public information mechanisms, in coalition formation games is derived. I also apply the results to International Environmental Agreements (IEAs), where a central authority, as an information sender, attempts to reduce the global level of greenhouse gases (GHG) by communication of information on social cost of GHG. 
Keywords:  Coalition Formation, Learning, Information Persuasion, International Environmental Agreements 
JEL:  D83 D70 C72 Q54 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2017.28&r=gth 
By:  Robin Nicole; Peter Sollich 
Abstract:  We study the distribution of strategies in a large game that models how agents choose among different double auction markets. We classify the possible mean field Nash equilibria, which include potentially segregated states where an agent population can split into subpopulations adopting different strategies. As the game is aggregative, the actual equilibrium strategy distributions remain undetermined, however. We therefore compare with the results of ExperienceWeighted Attraction (EWA) learning, which at long times leads to Nash equilibria in the appropriate limits of large intensity of choice, low noise (long agent memory) and perfect imputation of missing scores (fictitious play). The learning dynamics breaks the indeterminacy of the Nash equilibria. Nontrivially, depending on how the relevant limits are taken, more than one type of equilibrium can be selected. These include the standard homogeneous mixed and heterogeneous pure states, but also \emph{heterogeneous mixed} states where different agents play different strategies that are not all pure. The analysis of the EWA learning involves FokkerPlanck modeling combined with large deviation methods. The theoretical results are confirmed by multiagent simulations. 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1706.09763&r=gth 
By:  Kostyantyn Mazur 
Abstract:  This paper analyzes the structure of mixedstrategy equilibria for Colonel Blotto games, where the outcome on each battlefield is a polynomial function of the difference between the two players' allocations. This paper severely reduces the set of strategies that needs to be searched to find a Nash equilibrium. It finds that there exists a Nash equilibrium where both players' mixed strategies are discrete distributions, and it places an upper bound on the number of points in the supports of these discrete distributions. 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1706.08479&r=gth 
By:  Haim Shalit (BGU) 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:1701&r=gth 
By:  Marco A. Marini (University of Rome La Sapienza) 
Abstract:  This paper introduces a number of gametheoretic tools to model collusive agreements among firms in vertically differentiated markets. I firstly review some classical literature on collusion between two firms producing goods of exogenous different qualities. I then extend the analysis to a nfirm vertically differentiated market to study the incentive to form either a whole market alliance or partial alliances made of subsets of consecutive firms in order to collude in prices. Within this framework I explore the price behaviour of groups of colluding firms and their incentive to either pruning or proliferating their products. It is shown that a selective pruning within the cartel always occurs. Moreover, by associating a partition function game to the nfirm vertically differentiated market, it can be shown that a sufficient condition for the cooperative (or coalitional) stability of the whole industry cartel is the equidistance of firms’ products along the quality spectrum. Without this property, and in presence of large quality differences, collusive agreements easily lose their stability. In addition, introducing a standard infinitely repeatedgame approach, I show that an increase in the number of firms in the market may have contradictory effects on the incentive of firms to collude: it can make collusion easier for bottom and intermediate firms and harder for the top quality firm. Finally, by means of a threefirm example, I consider the case in which alliances can set endogenously qualities, prices and number of variants on sale. I show that, in every formed coalition, (i) market pruning dominates product proliferation and (ii) partial cartelisation always arises in equilibrium, with the bottom quality firm always belonging to the alliance. 
Keywords:  Vertically Differentiated Market, Price Collusion, Product Pruning, Product Proliferation, Endogenous Qualities, Endogenous Alliance Formation, Coalition Structures, Grand Coalition, Coalition Stability, Core, Simultaneous and Sequential Game of Coalition Formation 
JEL:  D42 D43 L1 L12 L13 L41 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2017.29&r=gth 