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on Game Theory |
| By: | Christian Ewerhart |
| Abstract: | Payoff security combined with reciprocal upper semicontinuity is sufficient for better-reply security, and consequently for the existence of a pure strategy Nash equilibrium in compact, quasiconcave games by Reny's (1999) theorem. Analogously, diagonal payoff security combined with upper semicontinuity of the diagonal payoff function has been widely understood to be sufficient for diagonal better-reply security, and consequently for the existence of a symmetric pure strategy Nash equilibrium in compact, diagonally quasiconcave, quasi-symmetric games. We show by example that this is incorrect. Specifically, diagonal better-reply security may fail to hold, and a symmetric pure strategy equilibrium may fail to exist, if some player's payoff function lacks lower semicontinuity, with respect to the opponents' symmetric strategy profile, at all strategy profiles reached from a non-equilibrium profile on the diagonal by a unilateral better response of that player. These difficulties disappear, both in the game and in its mixed extension, if the lower bound on a player's payoff in the definition of diagonal payoff security is raised to reflect the higher levels that arbitrary better responses may achieve. We also discuss the relationship between our strengthened condition and diagonal payoff security. |
| Keywords: | Discontinuous games, equilibrium existence, quasi-symmetric games, diagonal payoff security |
| JEL: | C62 C72 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:414&r= |
| By: | Vladimir Shikhman |
| Abstract: | For generalized Nash equilibrium problems (GNEP) with shared constraints we focus on the notion of normalized Nash equilibrium in the nonconvex setting. The property of nondegeneracy for normalized Nash equilibria is introduced. Nondegeneracy refers to GNEP-tailored versions of linear independence constraint qualification, strict complementarity and second-order regularity. Surprisingly enough, nondegeneracy of normalized Nash equilibrium does not prevent from degeneracies at the individual players' level. We show that generically all normalized Nash equilibria are nondegenerate. Moreover, nondegeneracy turns out to be a sufficient condition for the local uniqueness of normalized Nash equilibria. We emphasize that even in the convex setting the proposed notion of nondegeneracy differs from the sufficient condition for (global) uniqueness of normalized Nash equilibria, which is known from the literature. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.13878&r= |
| By: | Davidson Cheng |
| Abstract: | We propose a finite automaton-style solution concept for supergames. In our model, we define an equilibrium to be a cycle of state switches and a supergame to be an infinite walk on states of a finite stage game. We show that if the stage game is locally non-cooperative, and the utility function is monotonously decreasing as the number of defective agents increases, the symmetric multiagent prisoners' dilemma supergame must contain one symmetric equilibrium and can contain asymmetric equilibria. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.13772&r= |
| By: | Baranski, Andrzej; Geraldes, Diogo; Kovaliukaite, Ada; Tremewan, James |
| Abstract: | Women are underrepresented in political and business decision-making bodies across the world. To investigate the causal effect of gender representation on multilateral negotiations, we experimentally manipulate the composition of triads in a majoritarian, divide-the-dollar game. First, we find that inclusive splits and unanimous agreement rates are highest in all-female groups and lowest in all-male groups suggesting that female representation increases fairness. Second, we document a robust gender gap in earnings, driven largely by the exclusion of women from coalitions rather than differential shares within coalitions. Interestingly, we find that distinct bargaining dynamics can underlie the same inequitable outcomes: While gender-biased outcomes are sometimes caused by outright discrimination, they can also be driven by more complex dynamics related to gender differences in bargaining strategies. These different dynamics manifest in mixed-gender coalitions being less stable when the excluded party is male rather than female. |
| Keywords: | multilateral bargaining, gender gap, lab experiment |
| JEL: | C72 J16 J31 |
| Date: | 2022–04–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113063&r= |
| By: | Little, Andrew T. |
| Abstract: | The central puzzle of persuasion is why a receiver would ever listen to a sender who they know is trying to change their beliefs or behavior. This paper provides a common formal framework for five approaches to solving this puzzle: (1) some messages are easier to send for those with favorable information (costly signaling), (2) the sender and receiver have partially aligned interests (cheap talk), (3) the sender messages can be checked (verifiable information), (4) the sender cares about perceptions of his competence/honesty (reputation concerns), and (5) the sender can “commit” to a messaging strategy (Bayesian Persuasion). To explore the relative value of these approaches, I discuss which provide insight into prominent empirical findings on campaigns, partisan media/propaganda, and lobbying. While models focusing on commitment have rapidly become one of the most common (if not the most common) theoretical approach to studying persuasion in political science and economics in the past decade, they are not particularly well-suited to explaining these phenomena. |
| Date: | 2022–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:ygw8e&r= |
| By: | Andreas Bjerre-Nielsen; Martin Benedikt Busch |
| Abstract: | We investigate how individuals form expectations about population behavior using statistical inference based on observations of their social relations. Misperceptions about others' connectedness and behavior arise from sampling bias stemming from the friendship paradox and uncertainty from small samples. In a game where actions are strategic complements, we characterize the equilibrium and analyze equilibrium behavior. We allow for agent sophistication to account for the sampling bias and demonstrate how sophistication affects the equilibrium. We show how population behavior depends on both sources of misperceptions and illustrate when sampling uncertainty plays a critical role compared to sampling bias. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.13046&r= |
| By: | Arash Abizadeh; Adrian Vetta |
| Abstract: | A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose-Banzhaf measure, the classic Shapley-Shubik index, and the newly proposed Recursive Measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the Recursive Measure as a reasonable measure of voting power. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08368&r= |
| By: | Jonas von Wangenheim |
| Abstract: | Customer data enables online marketplaces to identify buyers’ preferences and provide individualized product information. Buyers learn their product value only after contracting when the product is delivered. I characterize the impact of such ex-ante information on buyer surplus and seller surplus, when the seller sets prices and refund conditions in response to the ex-ante information. I show that efficient trade and an arbitrary split of the surplus can be achieved. For the buyer-optimal signal low-valuation buyers remain partially uninformed. Such a signal induces sellers to sell at low prices without refund options, resulting in commonly observed practices of opaque sales. |
| Keywords: | information disclosure, sequential screening, information design, strategic learning, Bayesian persuasion, mechanism design, platform economics, consumer protection |
| JEL: | D82 D86 D18 |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_352&r= |
| By: | Herings, Jean-Jacques (Tilburg University, School of Economics and Management); Khan, Abhimanyu |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:03f2ece9-902b-4dba-a16e-0dfa9fc16a9e&r= |
| By: | Yash Deshpande; Elchanan Mossel; Youngtak Sohn |
| Abstract: | Bayesian models of group learning are studied in Economics since the 1970s and more recently in computational linguistics. The models from Economics postulate that agents maximize utility in their communication and actions. The Economics models do not explain the "probability matching" phenomena that are observed in many experimental studies. To address these observations, Bayesian models that do not formally fit into the economic utility maximization framework were introduced. In these models individuals sample from their posteriors in communication. In this work, we study the asymptotic behavior of such models on connected networks with repeated communication. Perhaps surprisingly, despite the fact that individual agents are not utility maximizers in the classical sense, we establish that the individuals ultimately agree and furthermore show that the limiting posterior is Bayes optimal. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.11561&r= |
| By: | David K Levine; Salvatore Modica; Aldo Rustichini |
| Date: | 2022–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:11694000000000112&r= |
| By: | Inderst, Roman; Sartzetakis, Eftichios S.; Xepapadeas, Anastasios |
| Abstract: | We analyze firms incentives to coordinate on the introduction of a more sustainable product variant when consumers preferences for greater sustainability depend on the perceived social norm, which in turn is shaped by average consumption behavior. Such preferences lead to multiple equilibria. If the more sustainable variant allows firms to sufficiently expand their aggregate market share, when a lenient legal regime makes this feasible they will coordinate on the more sustainable outcome. If their aggregate market share however does not expand sufficiently under the more sustainable variant, coordination can forestall a more sustainable outcome. Our analysis thus both confirms and qualifies the notion of a sustainability first-mover disadvantage as a justification for an agreement between competitors, which has gained traction in antitrust. We also provide empirical evidence for norm-based sustainability preferences. |
| Keywords: | Sustainability,Antitrust,Firm Cooperation |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esprep:259402&r= |