
on Game Theory 
By:  Eraslan, Hulya (Rice University) 
Abstract:  I study a multilateral sequential bargaining model among risk averse players in which the players may differ in their probability of being selected as the proposer and the rate at which they discount future payoffs. For games in which agreement requires less than unanimous consent, I characterize the set of stationary subgame perfect equilibrium payoffs. With this characterization, I establish the uniqueness of the equilibrium payoffs. For the case where the players have the same discount factor, I show that the payoff to a player is nondecreasing in his probability of being selected as the proposer. For the case where the players have the same probability of being selected as the proposer, I show that the payoff to a player is nondecreasing in his discount factor. This generalizes Eraslan [2002] by allowing the players to be risk averse. 
Date:  2015–05 
URL:  http://d.repec.org/n?u=RePEc:ecl:riceco:15001&r=all 
By:  Mitri Kitti (Department of Economics, University of Turku) 
Abstract:  Equilibrium payoffs corresponding to subgame perfect equilibria in pure strategies are characterized for infinitely repeated games with discounted payoffs. The equilibrium payoff set of a game is a fixedpoint of setvalued operators introduced in the paper. The new operator formalism is utilized in showing the folk theorem for repeated games with unequal but constant discount rates. When the players become more patient, the equilibrium payoff set converges to the fixedpoint of an asymptotic operator. This limit set corresponds to the subgame perfect equilibria of a continuoustime repeated game. It is shown that the limit set is convex, which implies that pure strategies are sufficient in obtaining all payoffs in the limit. However, this set differs from the set of all feasible and individually rational payoffs, when the discount rates are not equal. The limit sets for constant discount rates can be used in analyzing the outer limit of equilibrium payoffs when the discount factors increase but discount rates are not fixed. 
Keywords:  repeated game, equilibrium payoff set, folk theorem, unequal discount rates, continuoustime game 
JEL:  C72 C73 
Date:  2014–12 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp98&r=all 
By:  Hannu Salonen (Department of Economics, University of Turku) 
Abstract:  We investigate the cases when the Bonacich measures of strongly connected directed bipartite networks can be interpreted as a Nash equilibrium of a noncooperative game. One such case is a twoperson game such that the utility functions are bilinear, the matrices of these bilinear forms represent the network, and strategies have norm at most one. Another example is a twoperson game with quadratic utility functions. A third example is an m + n person game with quadratic utilitity functions, where the matrices representing the network have dimension m × n. For connected directed bipartite networks we show that the Bonacich measures are unique and give a recursion formula for the computation of the measures. The Bonacich measures of such networks can be interpreted as a subgame perfect equilibrium path of an extensive form game with almost perfect information. 
Keywords:  networks, influence measures, Nash equilibrium 
JEL:  C71 D85 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp100&r=all 
By:  Battaglini, Marco; Nunnari, Salvatore; Palfrey, Thomas R 
Abstract:  Most public goods are durable and have a significant dynamic component. In this paper, we report the results from a laboratory experiment designed explicitly to study the dynamics of free riding behavior in the accumulation of a durable public good that provides a stream of discounted benefits over a potentially infinite horizon. This dynamic freerider problem differs from static ones in fundamental ways and implies several economically important predictions that are absent in static frameworks. We consider two cases: economies with reversibility (RIE), where the agents’ voluntary contributions to the public good can be positive or negative; and economies with irreversibility (IIE), where contributions are non negative. For both economies, we characterize the unique Markov perfect equilibrium. The evidence supports the main predictions from the theory: behavior is generally consistent with stationary, forwardlooking behavior; both in RIE and IIE the accumulation path is inefficiently slow and the public good underprovided; and RIE induces significantly higher public good contributions than IIE. A number of interesting deviations from the theoretical predictions are observed: both in RIE and in IIE we have overinvestment in the early rounds of the game; in RIE overinvestment is followed by periods in which negative contributions correct the stock, bringing it back to the predicted steady state; in IIE overinvestment tends to decline approaching zero. To test the Markovian assumption, we compare the predictions of the Markov equilibrium with the prediction of the most efficient subgame perfect equilibrium and propose a novel experimental methodology that relies on the comparison between the behavior in the dynamic game and the behavior in a oneperiod reducedform version of the dynamic game. 
Keywords:  durable public goods; experiments; voluntary contribution mechanism 
JEL:  C72 C73 C78 C92 H41 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:10788&r=all 
By:  NISHIMURA, Takeshi; OKADA, Akira; SHIRATA, Yasuhiro 
Abstract:  Group formation is a fundamental activity in human society. Humans often exclude others from a group and divide the group benefit in a fair way only among group members. Such an allocation is called ingroup fair. Does natural selection favor an ingroup fair allocation? We investigate the evolution of fairness and group formation in a threeperson Ultimatum Game (UG) in which the group value depends on its size. In a stochastic model of the frequencydependent Moran process, natural selection favors the formation of a twoperson subgroup in the low mutation limit if its group value exceeds a high proportion (0.7) of that of the largest group. Stochastic evolutionary game theory provides theoretical support to explain the behavior of human subjects in economic experiments of a threeperson UG. 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:hit:econdp:201506&r=all 
By:  Yann Rébillé; Lionel Richefort 
Abstract:  We model a bipartite network in which links connect agents with public goods. Agents play a voluntary contribution game in which they decide how much to contribute to each public good they are connected to. We show that the problem of finding a Nash equilibrium can be posed as a nonlinear complementarity one. The existence of an equilibrium point is established for a wide class of individual preferences. We then find a simple sufficient condition, on network structure only, that guarantees the uniqueness of the equilibria, and provide an easy procedure for building networks that respects this condition. 
Date:  2014–10–15 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01074708&r=all 
By:  Heller, Yuval 
Abstract:  Various papers have presented folktheorem results that yield efficiency in the repeated Prisoner's Dilemma with imperfect private monitoring. I present a mild equilibrium refinement that requires robustness against small perturbations in the behavior of potential opponents, and I show that only defection satisfies this mild refinement among all the equilibria in the existing literature, unless one assumes either (1) communication among the players, or (2) sufficient correlation between the private signals (conditional on the actionprofile). 
Keywords:  Belieffree equilibrium, evolutionary stability, imperfect private monitoring, repeated Prisoner's Dilemma, communication. 
JEL:  C73 D82 
Date:  2015–08–08 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:64468&r=all 
By:  Sonja Brangewitz (University of Paderborn); ClausJochen Haake (University of Paderborn); Philipp Moehlmeier (Bielefeld University) 
Abstract:  We analyze the stability of networks when two intermediaries strategically form costly links to customers. We interpret these links as customer relationships that enable trade to sell a product. Equilibrium prices and equilibrium quantities on the output as well as on the input market are determined endogenously for a given network of customer relationships. We investigate in how far the substitutability of the intermediaries' products and the costs of link formation influence the intermediaries' equilibrium profits and thus have an impact on the incentives to strategically form relationships to customers. For networks with three customers we characterize locally stable networks, in particular existence is guaranteed for any degree of substitutability. Moreover for the special cases of perfect complements, independent products and perfect substitutes, local stability coincides with the stronger concept of Nash stability. Additionally, for networks with n customers we analyze stability regions for selected networks and determine their limits when n goes to infinity. It turns out that the shape of the stability regions for those networks does not significantly change compared to a setting with a small number of customers. 
Keywords:  Network Formation, Product Differentiation, Oligopoly, Quantity Competition 
JEL:  C70 D43 D85 L13 
Date:  2015–05 
URL:  http://d.repec.org/n?u=RePEc:pdn:ciepap:91&r=all 
By:  Tomoya Kazumura; Shigehiro Serizawa 
Abstract:  Consider the problem of allocating objects to agents and how much they should pay. Each agent has a preference relation over pairs of a set of objects and a payment. Preferences are not necessarily quasilinear. Nonquasilinear preferences describe environments where payments influence agents' abilities to utilize objects. This paper is to investigate the possibility of designing efficient and strategyproof rules in such environments. A preference relation is single demand if an agent wishes to receive at most one object; it is multi demand if whenever an agent receives one object, an additional object makes him better off. We show that if a domain contains all the single demand preferences and at least one multi demand preference relation, and there are more agents than objects, then no rule satisfies efficiency, strategyproofness, individual rationality, and no subsidy for losers on the domain. 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:0943&r=all 