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on Game Theory |
| By: | Evan M. Calford |
| Abstract: | We study the use of mixed strategies in games by ambiguity averse agents with a preference for randomization. Applying the decision theoretic model of Saito (2015) to games, we establish that the set of rationalizable strategies grows larger as preferences for randomization weaken. An agent’s preference for randomization is partially observable: given the behavior of an agent in a game, we can determine an upper bound on the strength of randomization preferences for that agent. Notably, data in previous experiments on ambiguity aversion in games is not consistent with a maximal preference for randomization for approximately 30% of subjects. |
| Keywords: | Ambiguity Aversion, Mixed Strategies, Game Theory |
| JEL: | D81 C70 C72 |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2020-675&r=all |
| By: | Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta |
| Abstract: | In a public good provision or a public bad abatement situation, the non-cooperative interplay of the participants typically results in low levels of provision or abatement. In the familiar class of n-person quadratic games, we show that Coarse Correlated equilibria (CCEs) - simple mediated communication devices that do not alter the strategic structure of the game - can significantly outperform the Nash equilibrium in terms of the policy objective above. |
| Keywords: | Quadratic game, Coarse correlated equilibrium, Abatement level, Efficiency gain |
| JEL: | C72 Q52 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:301895429&r=all |
| By: | Robert Simon; Stanislaw Spiez; Henryk Torunczyk |
| Abstract: | For a set-valued function $F$ on a compact subset $W$ of a manifold, spanning is a topological property that implies that $F(x) \ne 0$ for interior points $x$ of $W$. A myopic equilibrium applies when for each action there is a payoff whose functional value is not necessarily affine in the strategy space. We show that if the payoffs satisfy the spanning property, then there exist a myopic equilibrium (though not necessarily a Nash equilibrium). Furthermore, given a parametrized collection of games and the spanning property to the structure of payoffs in that collection, the resulting myopic equilibria and their payoffs have the spanning property with respect to that parametrization. This is a far reaching extension of the Kohberg-Mertens Structure Theorem. There are at least four useful applications, when payoffs are exogenous to a finite game tree (for example a finitely repeated game followed by an infinitely repeated game), when one wants to understand a game strategically entirely with behaviour strategies, when one wants to extends the subgame concept to subsets of a game tree that are known in common, and for evolutionary game theory. The proofs involve new topological results asserting that spanning is preserved by relevant operations on set-valued functions. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.12876&r=all |
| By: | Bodoff, David |
| Abstract: | People’s ability to coordinate on salient labels has been widely reported since Schelling. However, it is not known how players behave when label salience conflicts with payoff dominance. We consider such games by independently varying the two elements, focusing especially on cases where the two criteria conflict. We also introduce a new form of the game, in which players choose labeled strategies in response to a stimulus. In games with no reference stimulus, behavior is consistent with a simple model, according to which strategic players assume their naïve counterparts choose the higher payoff. In games with a reference stimulus, behavior is consistent with a model in which strategic players assume their naïve counterparts choose the label that is more salient to them, except perhaps where the two labels’ salience are very similar, in which case the higher payoff is chosen. A key finding is that in the presence of a stimulus, play is best explained by a model in which players choose according to label salience, even against the combination of payoff and risk dominance. |
| Keywords: | coordination games; focal points; cognitive hierarchy; |
| JEL: | C70 C72 |
| Date: | 2020–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:102213&r=all |
| By: | Salvadori, Neri; De Francesco, Massimo A. |
| Abstract: | This paper studies Bertrand-Edgeworth competition among firms producing a homogeneous commodity under efficient rationing and constant (andidentical across firms) marginal cost until full capacity utilization is reached. Our focus is on a subset of the no pure-strategy equilibrium region of the capacity space in which, in a well-defined sense, some firms are large and the others are small. We characterize equilibria for such subset. For each firm, the payoffs are the same at any equilibrium and, for each type of firm, they are proportional to capacity. While there is a single profile of equilibrium distributions for the large firms, there is a continuum of equilibrium distributions for the small firms: what is uniquely determined, for the latter, is the capacity-weighted sum of their equilibrium distributions and hence the union of the supports of their equilibrium strategies. |
| Keywords: | Bertrand-Edgeworth oligopoly; mixed strategy equilibrium; large and small firms |
| JEL: | C72 D43 L13 |
| Date: | 2020–08–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:102274&r=all |
| By: | Streekstra, Leanne (Department of Business and Economics); Trudeau, Christian (Department of Economics) |
| Abstract: | We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We show that the resulting cost sharing problem always has a non-empty core, regardless of the number of agents and periods, the cost structure or the demand profile. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain non-vacuity results for the cores of source-connection problems, (m-sided) assignment problems and minimum coloring problems. |
| Keywords: | Shortest path; demand over multiple periods; cooperative game; core; source-connection; assignment |
| JEL: | C71 D63 |
| Date: | 2020–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2020_007&r=all |
| By: | Zijun Wu; Rolf H. Moehring; Chunying Ren; Dachuan Xu |
| Abstract: | This paper provides a comprehensive convergence analysis of the PoA of both pure and mixed Nash equilibria in atomic congestion games with unsplittable demands. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.14769&r=all |
| By: | Shaofei Jiang |
| Abstract: | Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (2017) propose to focus on truth-leaning equilibria, i.e., perfect Bayesian equilibria where the sender prefers disclosing truthfully when indifferent, and the receiver takes off-path disclosure at face value. They show that a truth-leaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truth-telling. We show that, when the receiver's action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receiver's payoff. A purifiable equilibrium is a truth-leaning equilibrium in an infinitesimally disturbed game. It exists and features a simple characterization. A truth-leaning equilibrium that is also purifiable is an equilibrium of the perturbed game. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.06403&r=all |
| By: | Anna Bayona; Oana Peia |
| Abstract: | We design a laboratory experiment to test the importance of wealth as a channel for financial contagion across markets with unrelated fundamentals. Specifically, in a sequential global game, we analyze the decisions of a group of investors that hold assets in two markets. We consider two treatments that vary the level of diversification of these assets across markets, which allows us to disentangle the wealth effect from other sources of financial contagion. We provide evidence of contagion due to a wealth effect when investors have completely diversified portfolios. In this treatment, for certain ranges of fundamentals, we show that a coordination failure in the first market reduces investors' wealth, which makes them more likely to withdraw their investments in the second market, thereby increasing the probability of a crisis. |
| Keywords: | Financial contagion; Financial crises; Wealth; Coordination games; Global games |
| JEL: | C72 C92 D8 G01 G11 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:ucn:wpaper:202007&r=all |
| By: | Weston Barger; Ryan Donnelly |
| Abstract: | We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model, equilibrium is characterized by the unique root of a particular polynomial. Analysis of this polynomial with small levels of risk-aversion and transaction costs reveal a dimensionless parameter which captures several orders of asymptotic accuracy of the equilibrium behaviour. In a continuous time analogue of the single auction model, incorporation of a transaction costs allows the informed agent's optimal trading strategy to be obtained in feedback form. Linear equilibrium is characterized by the unique solution to a system of two ordinary differential equations, of which one is forward in time and one is backward. When transaction costs are in effect, the price set by the market maker in equilibrium is not fully revealing of the informed agent's private signal, leaving an information gap at the end of the trading interval. When considering vanishing transaction costs, the equilibrium trading strategy and pricing rules converge to their frictionless counterparts. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.14162&r=all |
| By: | Tiziano De Angelis; Nikita Merkulov; Jan Palczewski |
| Abstract: | We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag measurable processes. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyond the variational methods (based on PDEs) developed in the related literature on Dynkin games in continuous time with partial/asymmetric information. Instead, we focus on a probabilistic and functional analytic approach based on the general theory of stochastic processes and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp. 171-176). Our framework encompasses examples found in the literature on continuous time Dynkin games with asymmetric information and we provide counterexamples to show that our assumptions cannot be further relaxed. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.10643&r=all |
| By: | Nicole B\"auerle; Alexander Glauner |
| Abstract: | We consider robust Markov Decision Processes with Borel state and action spaces, unbounded cost and finite time horizon. Our formulation leads to a Stackelberg game against nature. Under integrability, continuity and compactness assumptions we derive a robust cost iteration for a fixed policy of the decision maker and a value iteration for the robust optimization problem. Moreover, we show the existence of deterministic optimal policies for both players. This is in contrast to classical zero-sum games. In case the state space is the real line we show under some convexity assumptions that the interchange of supremum and infimum is possible with the help of Sion's minimax Theorem. Further, we consider the problem with special ambiguity sets. In particular we are able to derive some cases where the robust optimization problem coincides with the minimization of a coherent risk measure. In the final section we discuss two applications: A robust LQ problem and a robust problem for managing regenerative energy. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.13103&r=all |
| By: | Sanjit Dhami; Emma Manifold; Ali al-Nowaihi |
| Abstract: | We propose a theoretical model that embeds social identity concerns, as in Akerlof and Kranton (2000), with inequity averse preferences, as in Fehr and Schmidt (1999). We conduct an artefactual ultimatum game experiment with registered members of British political parties, for whom political identity is salient and redistribution is also likely to be salient. The empirical results are as follows. (1) Proposers and responders demonstrate ingroup-favoritism. (2) Proposers exhibit quantitatively stronger social identity effects relative to responders. (3) As redistributive taxes increase, average offers by proposers and the average minimum acceptable offers of responders (both as a proportion of income) decline by almost the same amount, suggesting a shared understanding that is characteristic of social norms. (4) Subjects experience less disadvantageous inequity from ingroup members relative to outgroup members. |
| Keywords: | social identity, political identity, prosocial behavior, ultimatum game, fiscal redistribution, entitlements |
| JEL: | D01 D03 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8397&r=all |
| By: | Egor Starkov (University of Copenhagen) |
| Abstract: | This paper explores a model of dynamic signaling without commitment. It is known that separating equilibria do not exist if the sender cannot commit to future costly actions, since no single action can have enough weight to be an effective signal. This paper, however, shows that informative and payoff-relevant signaling can occur even without commitment and without resorting to unreasonable off-path beliefs. Such signaling can only happen through attrition, when the weakest type mixes between revealing own type and pooling with the stronger types. The possibility of full information revelation in the limit hence depends crucially on the assumptions about the state space. We illustrate the results by exploring a model of dynamic price signaling and show that prices may be informative of product quality even if the seller cannot commit to future prices, with both high and low prices being able to signal high quality. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.09568&r=all |
| By: | Siddhartha Bandyopadhyay; Antonio Cabrales |
| Abstract: | We consider a model where agents differ in their `types' which determines their voluntary contribution towards a public good. We analyze what the equilibrium composition of groups are under centralized and centralized choice. We show that there exists a top-down sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by level of types, with the first k types in the group with the highest price and so on. This exists both under decentralized and centralized choosing. We also analyze the model with endogenous group size and examine under what conditions is top-down sorting socially efficient. We illustrate when integration (i.e. mixing types so that each group's average type if the same) is socially better than top-down sorting. Finally, we show that top down sorting is efficient even when groups compete among themselves. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.03102&r=all |
| By: | Gonzalo Cisternas; Aaron Kolb |
| Abstract: | We study dynamic signaling when the informed party does not observe the signals generated by her actions. A long-run player signals her type continuously over time to a myopic second player who privately monitors her behavior; in turn, the myopic player transmits his private inferences back through an imperfect public signal of his actions. Preferences are linear-quadratic and the information structure is Gaussian. We construct linear Markov equilibria using belief states up to the long-run player's $\textit{second-order belief}$. Because of the private monitoring, this state is an explicit function of the long-run player's past play. A novel separation effect then emerges through this second-order belief channel, altering the traditional signaling that arises when beliefs are public. Applications to models of leadership, reputation, and trading are examined. |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2007.15514&r=all |
| By: | Xu, Lili; Lee, Sang-Ho |
| Abstract: | This study investigates government public policies facing competing firms’ strategic corporate social responsibility (CSR) activities and finds that the choice of CSR crucially depends on corporate profit tax. We demonstrate that strategic CSR decreases while social welfare increases with corporate tax. When the government grants uniform output subsidies, we show that bilateral CSR leads to a lower CSR level than under unilateral CSR but bilateral CSR is always beneficial to society. However, when the government grants discriminatory output subsidies which yield different levels of unilateral CSR, we show that domestic CSR leads to a lower CSR level than under foreign CSR. In an endogenous CSR choice game, domestic CSR (no CSR) is a Nash equilibrium when corporate tax is low (high) under the uniform subsidy, while foreign CSR could be a Nash equilibrium when corporate tax is low under the discriminatory subsidy. |
| Keywords: | corporate profit tax; corporate social responsibility; endogenous CSR choice game |
| JEL: | D43 H21 L21 |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:102313&r=all |