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on Game Theory |
| By: | Costas Cavounidis; Sambuddha Ghosh; Johannes H\"orner; Eilon Solan; Satoru Takahashi |
| Abstract: | We apply Blackwell optimality to repeated games. An equilibrium whose strategy profile is sequentially rational for all high enough discount factors simultaneously is a Blackwell (subgame-perfect, perfect public, etc.) equilibrium. The bite of this requirement depends on the monitoring structure. Under perfect monitoring, a ``folk'' theorem holds relative to an appropriate notion of minmax. Under imperfect public monitoring, absent a public randomization device, any perfect public equilibrium generically involves pure action profiles or stage-game Nash equilibria only. Under private conditionally independent monitoring, in a class of games that includes the prisoner's dilemma, the stage-game Nash equilibrium is played in every round. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.05481 |
| By: | Simon Martin; Hans-Theo Normann; Paul P\"uplichhuisen; Tobias Werner |
| Abstract: | We study the propensity of independent algorithms to collude in repeated Cournot duopoly games. Specifically, we investigate the predictive power of different oligopoly and bargaining solutions regarding the effect of asymmetry between firms. We find that both consumers and firms can benefit from asymmetry. Algorithms produce more competitive outcomes when firms are symmetric, but less when they are very asymmetric. Although the static Nash equilibrium underestimates the effect on total quantity and overestimates the effect on profits, it delivers surprisingly accurate predictions in terms of total welfare. The best description of our results is provided by the equal relative gains solution. In particular, we find algorithms to agree on profits that are on or close to the Pareto frontier for all degrees of asymmetry. Our results suggest that the common belief that symmetric industries are more prone to collusion may no longer hold when algorithms increasingly drive managerial decisions. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.07178 |
| By: | Nadia Gui\~naz\'u; Pablo Neme; Jorge Oviedo |
| Abstract: | This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and commitments vary. Specifically, we analyze a dynamic matching game in which firms make offers to workers in each period, considering three types of commitment: (i) no commitment from either side, (ii) firms' commitment, and (iii) workers' commitment. Our results demonstrate that stable matchings can be supported as stationary equilibria under different commitment scenarios, depending on the strategies adopted by firms and workers. Furthermore, we identify key conditions, such as discount factors, that influence agents' decisions to switch partners, thereby shaping equilibrium outcomes. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.19372 |
| By: | Daniel Luo; Alexander Wolitzky |
| Abstract: | We study reputation formation where a long-run player repeatedly observes private signals and takes actions. Short-run players observe the long-run player's past actions but not her past signals. The long-run player can thus develop a reputation for playing a distribution over actions, but not necessarily for playing a particular mapping from signals to actions. Nonetheless, we show that the long-run player can secure her Stackelberg payoff if distinct commitment types are statistically distinguishable and the Stackelberg strategy is confound-defeating. This property holds if and only if the Stackelberg strategy is the unique solution to an optimal transport problem. If the long-run player's payoff is supermodular in one-dimensional signals and actions, she secures the Stackelberg payoff if and only if the Stackelberg strategy is monotone. An application of our results provides a reputational foundation for a class of Bayesian persuasion solutions when the sender has a small lying cost. Our results extend to the case where distinct commitment types may be indistinguishable but the Stackelberg type is salient under the prior. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.15317 |
| By: | Guo, F.; Choi, S.; Goyal, S.; Moisan, F. |
| Abstract: | Social networks shape individual behavior, and public policy increasingly leverages networks to enhance effectiveness. It is therefore important to understand how individuals behave in network interactions. This paper uses lab experiments to examine behavior in games on networks involving strategic substitutes and strategic complements. Theory suggests that an individual’s choice is proportional to their (Bonacich) centrality. Our experiments, however, find that while choices increase with centrality, the relationship is weaker than predicted. The total action levels individuals choose and the total payoff they achieve are higher than the Nash outcomes in some cases while lower in others. We find that these results can be coherently explained by individuals’ behavioral attenuation: they have incomplete adjustments to the strategic differences across network positions, exhibiting a bias toward generally high-payoff choices in complex networks—even when these choices are not optimal for their specific network positions. |
| Keywords: | Centrality, Behavioural Biases, Networks |
| JEL: | C92 D83 D85 Z13 |
| Date: | 2024–12–31 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camjip:2433 |
| By: | Stringhi, Alessandro; Gil-Gallen, Sara; Albertazzi, Andrea |
| Abstract: | This paper studies how competition between groups affects cooperation. In the control condition, pairs of subjects play an indefinitely repeated Prisoner’s Dilemma game without external competition. In the treatment, two pairs compete against each other. No monetary rewards are tied to winning, isolating the bare impact of competition. In the treatment, cooperation increases by 16 percentage points. Strategies estimation shows a shift from selfish strategies (Always Defect) to cooperative ones (Grim Trigger). A theoretical model provides a rationale for the experimental results. |
| Keywords: | Institutional and Behavioral Economics |
| Date: | 2025–01–21 |
| URL: | https://d.repec.org/n?u=RePEc:ags:feemwp:349168 |
| By: | Steven Campbell; Marcel Nutz |
| Abstract: | We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas without regularization, there is no equilibrium. We prove that existence is restored if (and only if) a very particular, time-dependent cost on block trades is added to the model. In that case, the equilibrium is particularly tractable. We show that this equilibrium is the limit of the regularized equilibria as the instantaneous cost parameter $\varepsilon$ tends to zero. Moreover, we explain the seemingly ad-hoc block cost as the limit of the equilibrium instantaneous costs. Notably, in contrast to the single-player problem, the optimal instantaneous costs do not vanish in the limit $\varepsilon\to0$. We use this tractable equilibrium to study the cost of liquidating in the presence of predators and the cost of anarchy. Our results also give a new interpretation to the erratic behaviors previously observed in discrete-time trading games with transient price impact. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.09638 |
| By: | Yi Liu; Yang Yu |
| Abstract: | This paper explores the problem of mediated communication enhanced by money-burning tactics for commitment power. In our model, the sender has state-independent preferences and can design a communication mechanism that both transmits messages and burns money. We characterize the sender's maximum equilibrium payoff, which has clear geometric interpretations and is linked to two types of robust Bayesian persuasion. We demonstrate that, generically, the money-burning tactic \emph{strictly} improves the sender's payoff for almost all prior beliefs where commitment is valuable for the sender. Furthermore, our communication model directly applies to Web 3.0 communities, clarifying the commitment value within these contexts. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.19431 |
| By: | Harsh Shah; Jayakrishnan Nair; D Manjunath; Narayan Mandayam |
| Abstract: | We consider the following Colonel Blotto game between parties $P_1$ and $P_A.$ $P_1$ deploys a non negative number of troops across $J$ battlefields, while $P_A$ chooses $K, $ $K |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.06222 |
| By: | Vesa Kanniainen; Juha-Matti Lehtonen |
| Abstract: | Following Russia’s attack on Ukraine on February 24, 2022, Western countries have been providing military assistance to Ukraine. However, relative to GDP, the support from the small Baltic and Nordic countries has been greater than that of the larger European NATO countries. This article introduces first an alliance model to examine the incentive for alliance member countries to invest in their own national security in a deterrence equilibrium with no warfare. It is shown that an underinvestment incentive arises. The Russian invasion to Ukraine changed the rules of the game. Therefore, the article offers an explanation for the distribution of Ukrainian military assistance based on the national security classification of European NATO member states in a two-stage game-theoretic model. This distribution turns out to be conditional on the expectations associated with the second stage of the war game if Russia wins the war in its first stage and if there is uncertainty about NATO's ability to commit to its Article 5 to provide security to all of its members. |
| Keywords: | military aid to Ukraine, alliance theory, NATO, two-stage game |
| JEL: | D72 D74 H56 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11609 |
| By: | E. Emanuel Rapsch |
| Abstract: | A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional "nature" agent, this framework uses a single lottery draw to select a tree of a given decision forest. Each "personal" agent receives dynamic updates from an own oracle on the lottery outcome and makes partition-refining choices adapted to this information. This theory addresses a key limitation of existing approaches in extensive form theory, which struggle to model continuous-time stochastic processes, such as Brownian motion, as outcomes of "nature" decision making. Additionally, a class of stochastic extensive forms based on time-indexed action paths is constructed, encompassing a wide range of models from the literature and laying the groundwork for an approximation theory for stochastic differential games in extensive form. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.17587 |
| By: | Xiaoming Wang |
| Abstract: | In many non-cooperative settings, agents often possess useful information that provide an advantage over their opponent(s), but acting on such information too frequently can lead to detection. I develop a simple framework to analyze such a trade-off and characterize the optimal way in which to act on information. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.10564 |
| By: | Aggey Simons (Department of Economics, University of Ottawa, Canada) |
| Abstract: | This paper examines the stationarity of optimal contracts in infinitely repeated principal–agent relationships under complete information and enforcement constraints. We demonstrate that stationarity emerges as a robust feature of optimal contracts when agent types and actions are fully observable, and contract enforcement is supported by both public remedies and private termination threats. Under complete information, the trade-offs between enforcement costs and relational value become significantly simplified, resulting in stationary outcomes even when enforcement constraints are binding. These findings offer insights into contract design in environments where non-stationary profiles are either impractical or prohibitively costly. |
| Keywords: | dynamic contracts, contract enforcement, stationarity, complete information. |
| JEL: | D82 D86 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ott:wpaper:2501e |