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on Game Theory |
| By: | Takashi Ui (Department of Economics, Hitotsubashi University); Stephen Morris (Department of Economics, Massachusetts Institute of Technology) |
| Abstract: | Consider an analyst who models a strategic situation in terms of an incomplete information game and makes a prediction about players’ behavior. The analyst’s model approximately describes each player’s hierarchies of beliefs over payoff-relevant states, but the true incomplete information game may have correlated duplicated belief hierarchies, and the analyst has no information about the correlation. Under these circumstances, a natural candidate for the analyst’s prediction is the set of belief-invariant Bayes correlated equilibria (BIBCE) of the analyst’s incomplete information game. We introduce the concept of robustness for BIBCE: a subset of BIBCE is robust if every nearby incomplete information game has a BIBCE that is close to some BIBCE in this set. Our main result provides a sufficient condition for robustness by introducing a generalized potential function of an incomplete information game. A generalized potential function is a function on the Cartesian product of the set of states and a covering of the action space which incorporates some information about players’ preferences. It is associated with a belief-invariant correlating device such that a signal sent to a player is a subset of the player’s actions, which can be interpreted as a vague prescription to choose some action from this subset. We show that, for every belief-invariant correlating device that maximizes the expected value of a generalized potential function, there exists a BIBCE in which every player chooses an action from a subset of actions prescribed by the device, and that the set of such BIBCE is robust, which can differ from the set of potential maximizing BNE. |
| Keywords: | Bayes correlated equilibria, belief hierarchies, belief invariance, generalized potentials, incomplete information games, potential games |
| JEL: | C72 D82 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:upd:utmpwp:019&r=all |
| By: | Simone Cerreia-Vioglio; Fabio Maccheroni; David Schmeidler |
| Abstract: | We add here another layer to the literature on nonatomic anonymous games started with the 1973 paper by Schmeidler. More specifically, we define a new notion of equilibrium which we call $\varepsilon$-estimated equilibrium and prove its existence for any positive $\varepsilon$. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk--Nash. This augmented scope is our main motivation. At the same time, our approach also resolves some conceptual problems present in Schmeidler (1973), pointed out by Shapley. In that paper\ the existence of pure-strategy Nash equilibria has been proved for any nonatomic game with a continuum of players, endowed with an atomless countably additive probability. But, requiring Borel measurability of strategy profiles may impose some limitation on players' choices and introduce an exogenous dependence among\ players' actions, which clashes with the nature of noncooperative game theory. Our suggested solution is to consider every subset of players as measurable. This leads to a nontrivial purely finitely additive component which might prevent the existence of equilibria and requires a novel mathematical approach to prove the existence of $\varepsilon$-equilibria. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.01839&r=all |
| By: | Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)); Saulle, Riccardo; Seel, Christian (RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)) |
| Abstract: | This paper studies coalition formation among individuals who differ in productivity. The output of a coalition is determined by the sum of the productivities and the size of the coalition. We consider egalitarian societies in which coalitions split their surplus equally and individualistic societies in which the surplus of a coalition is split according to productivity. Preferences of coalition members depend on their material payoffs, but are also influenced by relative payoff concerns, which relate their material payoffs to the average material payoff in the coalition. Our analysis uses two stability notions, the Core and the Myopic Stable Set. The stable partitions in both egalitarian and individualistic societies are segregated, i.e., individuals with adjacent productivities form coalitions. If some individuals are not part of a productive coalition, then these are the least productive ones for egalitarian societies and the most productive ones for individualistic societies. If all individuals have different productivity levels and there are sufficient complementarities in production, egalitarian societies induce more efficiency than individualistic societies. |
| JEL: | C70 C71 D62 |
| Date: | 2020–03–26 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2020011&r=all |
| By: | Dang, Chuangyin; Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)); Li, Peixuan |
| Abstract: | Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP. |
| JEL: | C62 C72 C73 |
| Date: | 2020–02–17 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2020001&r=all |
| By: | Kerman, Toygar (RS: GSBE other - not theme-related research, General Economics 1 (Micro)); Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)); Karos, Dominik (RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)) |
| Abstract: | A Sender wants to persuade multiple Receivers with homogeneous preferences and a common belief about the state of the world to vote in favor of a proposal. Prior to the vote Sender commits to a communication strategy which sends private, potentially correlated, signals to Receivers that are contingent on the true state of the world. While Sender benefits from using private messages rather than public communication if Receivers vote sincerely, under the optimal communication strategy, sincere voting is not in any Receiver’s best interest. If the proposal does not require unanimous agreement, Sender’s optimal communication strategy after which sincere voting indeed constitutes a Bayes-Nash equilibrium is such that no voter is ever pivotal. |
| JEL: | C72 D72 D82 D83 |
| Date: | 2020–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2020004&r=all |
| By: | Kunimoto, Takashi (School of Economics, Singapore Management University); Saran, Rene (University of Cincinnati) |
| Abstract: | A social choice function (SCF) is robustly implementable in rationalizable strate-gies if every rationalizable strategy profile on every type space results in outcomes consistent with it. First, we establish an equivalence between robust implementation in rationalizable strategies and “weak rationalizable implementation”. Second, using the equivalence result, we identify weak robust monotonicity as a necessary and al-most sufficient condition for robust implementation in rationalizable strategies. This exhibits a contrast with robust implementation in interim equilibria, i.e., every equilib-rium on every type space achieves outcomes consistent with the SCF. Bergemann and Morris (2011) show that strict robust monotonicity is a necessary and almost sufficient condition for robust implementation in interim equilibria. We argue that strict robust monotonicity is strictly stronger than weak robust monotonicity, which further implies that, within general mechanisms, robust implementation in rationalizable strategies is more permissive than robust implementation in interim equilibria. The gap between robust implementation in rationalizable strategies and that in interim equilibria stems from the strictly stronger nonemptiness requirement inherent in the latter concept. |
| Keywords: | Ex post incentive compatibility; rationalizability; interim equilibrium; robust implementation; weak rationalizable implementation; weak robust monotonicity |
| JEL: | C72 D78 D80 |
| Date: | 2020–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2020_010&r=all |
| By: | Marta Montinaro (University of Salento); Rupayan Pal (Indira Gandhi Institute of Development Research); Marcella Scrimitore (University of Salento) |
| Abstract: | In a context of product innovation, we study two-part tariff licensing between a patentee and a potential rival which compete in a differentiated product market characterized by network externalities. The latter are shown to crucially affect the relative profitability of Cournot vs. Bertrand when a per unit royalty is applied. By contrast, we find that Cournot yields higher profits than Bertrand under ad valorem royalties, regardless of the strength of network effects. |
| Keywords: | Licensing, Product Innovation, Bertrand, Cournot, Network Effects |
| JEL: | L13 L20 D43 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2020-014&r=all |
| By: | J{\o}rgen Vitting Andersen; Philippe de Peretti |
| Abstract: | We introduce a new methodology that enables detection of the onset of convergence towards Nash equilibria in simple repeated games with infinitely large strategy spaces, thereby revealing the heuristics used in decision-making. The method works by constraining on a special finite subset of strategies, called decoupled strategies. We show how the technique can be applied to understand price formation in financial market experiments by introducing a predictive measure {\Delta}D: the different between positive decoupled strategies (recommending to buy) and negative decoupled strategies (recommending to sell). Using {\Delta}D we illustrate how the method can predict (at certain special times) participants' actions with a high success rate in a series of experiments |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.02337&r=all |
| By: | Akerlof, Robert (University of Warwick); Li, Hongyi (UNSW Business School); Yeo, Jonathan (University of Warwick) |
| Abstract: | This paper uses a laboratory experiment to study competitions for power — and the role of patronage in such competitions. We construct and analyze a new game — the “chicken-and-egg game” — in which chickens correspond to positions of power andeggsarethegame’scurrency. Wefindthatpowertendstoaccumulate,througha “power begets power” dynamic, in the hands of “lords.” Other subjects behave like their vassals in the sense that they take lords’ handouts rather than compete against them. We observe substantial wealth inequality as well as power inequality. There are also striking gender differences in outcomes — particularly in rates of lordship. In a second treatment, where we eliminate patronage by knocking out the ability to transfer eggs, inequality is vastly reduced and the “power begets power” dynamic disappears. |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wcreta:56&r=all |
| By: | Christian Ewerhart; Sheng Li |
| Abstract: | It is a common experience for present-day consumers making an international payment via credit or debit card to be invited to choose the currency in which they wish to have the transaction executed. While this choice, made feasible by a technology known as dynamic currency conversion (DCC), seems to foster competition, we show that the opposite is the case. In fact, the unique pure-strategy Nash equilibrium in a natural fee-setting game turns out to be highly asymmetric, entailing fees for the service provider that always exceed the monopoly level. Although losses in welfare may be substantial, a regulatory solution is unlikely to come about due to a global free-rider problem. |
| Keywords: | Dynamic currency conversion, payment cards, ambiguity aversion, price competition, monopoly, free-rider problem |
| JEL: | D21 G21 G28 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:345&r=all |