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on Game Theory |
| By: | Tadashi SEKIGUCHI; Katsutoshi WAKAI |
| Abstract: | Game theory proves the existence of a stronger punishment than the Nash reversion in the repeated games. Recent empirical ndings in Oligopoly, how- ever, suggest the implementation of the Nash reversion. In a standard repeated game setting, we propose a potential answer for this empirical puzzle by using a re ned version of the discounted utility that exhibits gain/loss asymmetry, where players discount gains more than losses. Our main result is as follows: among gain/loss robust subgame perfect equilibria, the Nash reversion o¤ers the strongest punishment. The robustness is based on the assumption that players are unsure about their own level of gain/loss asymmetry and choose only the strategies that are subgame perfect for any level of gain/loss asymmetry they can perceive as possible. |
| Keywords: | Gain/loss asymmetry, optimal penal code, repeated game, re-cursive utility, utility smoothing |
| JEL: | C73 D20 D90 L13 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:kue:epaper:e-24-009 |
| By: | Fedor Sandomirskiy; Po Hyun Sung; Omer Tamuz; Ben Wincelberg |
| Abstract: | We study finite normal-form games under a narrow bracketing assumption: when players play several games simultaneously, they consider each one separately. We show that under mild additional assumptions, players must play either Nash equilibria, logit quantal response equilibria, or their generalizations, which capture players with various risk attitudes. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.11243 |
| By: | Pierre Bardier |
| Abstract: | We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree to which rules satisfy an axiom, as well as several axioms, on the basis of a probability measure over the inputs of the rules. Armed with this notion of degree, we propose and characterize i) a criterion to evaluate and compare rules given a set of axioms, allowing the importance of each combination of axioms to differ, and ii) a criterion to measure the compatibility between given axioms, building on a analogy with cooperative game theory. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.13850 |
| By: | Claus-Jochen Haake (Paderborn University); Martin R. Schneider (Paderborn University) |
| Abstract: | The Banzhaf power index can be used to quantify the explanatory power of single conditions in a configurational analysis that aims at identifying whether combinations of conditions are sufficient for an outcome. The latter method is an integral part of the Qualitative Comparative Analysis (QCA) approach. It is widely used in the literature, e.g., in the field of International Management. Haake and Schneider (2023) give a rigorous description of the connection between the empirical and game theoretic modeling. To justify that the Banzhaf index is an appropriate tool to measure the influence of a condition, this paper discusses a novel axiomatization of the Banzhaf index that uses axioms that are directly linked to the QCA methodology. As a side result, we demonstrate that in our model the Banzhaf index can be reinterpreted as an average of Shapley-Shubik indices. |
| Keywords: | Banzhaf index, axiomatization, QCA, explanatory power |
| JEL: | C71 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:ciepap:162 |
| By: | Benjamin Golub |
| Abstract: | Square matrices often arise in microeconomics, particularly in network models addressing applications from opinion dynamics to platform regulation. Spectral theory provides powerful tools for analyzing their properties. We present an accessible overview of several fundamental applications of spectral methods in microeconomics, focusing especially on the Perron-Frobenius Theorem's role and its connection to centrality measures. Applications include social learning, network games, public goods provision, and market intervention under uncertainty. The exposition assumes minimal social science background, using spectral theory as a unifying mathematical thread to introduce interested readers to some exciting current topics in microeconomic theory. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.12309 |