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on Game Theory |
| By: | Christopher Graser (University of Amsterdam); Matthijs van Veelen (University of Amsterdam) |
| Abstract: | We consider the repeated prisoner’s dilemma with implementation errors, and look at the resulting population dynamics, both analytically and with simulations. We show that with implementation errors, pure equilibrium strategies represented by finite state automata exhibit a structure that we call self-mirroring. Because selection easily spreads thinly on subgames that are reached after (multiple) errors, we find that in the simulations, strategies are often not best respond- ing in all subgames. We also explore how forgiveness and cooperation respond to changes in the error rate and the continuation probability. Close to an error rate of 0, both show a hump-shaped pattern. We also explore how forgiveness and cooperation change with the error rate in models with a limited strategy set, and we have results for forgiveness at high error rates and/or low continuation probabilities. |
| JEL: | C73 |
| Date: | 2024–04–05 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240022 |
| By: | Subhadip Chakrabarti; Robert P Gilles; Lina Mallozzi |
| Abstract: | In this note we develop a generalisation of the $\lambda$-Core solution for non-cooperative games in normal form. We show that this generalised $\lambda$-Core is non-empty for the class of separable games that admit a socially optimal Nash equilibrium. Examples are provided that indicate that non-emptiness of the generalised $\lambda$-Core cannot be expected for large classes of normal form games. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06086 |
| By: | Zhengxing Zou (Beijing Jiaotong University and University of Toronto); René van den Brink (Vrije Universiteit Amsterdam); Yukihiko Funaki (Waseda University) |
| Abstract: | We propose and characterize weighted-egalitarian values for cooperative transferable utility games. Each weighted-egalitarian value divides the worth of the grand coalition into two parts and allocates them through equality and proportionality based on exogenous player weights. We characterize the family of all weighted-egalitarian values by employing the standard axioms of efficiency and linearity, in addition to two novel axioms: ω-ratio invariance for symmetric players and symmetry in weights. We then show that relaxing linearity to additivity and adding coalitional monotonicity results in a sub- family of affine combinations of equal division and weighted division values. Furthermore, using an axiom called monotonicity in weights, we characterize the family of convex combinations of equal division and weighted division values. |
| Keywords: | cooperative game, axiomatization, equal division value, weighted division value, equality |
| JEL: | C71 |
| Date: | 2024–03–26 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240021 |
| By: | Yufan Chen; Lan Wu; Renyuan Xu; Ruixun Zhang |
| Abstract: | Motivated by recent empirical findings on the periodic phenomenon of aggregated market volumes in equity markets, we aim to understand the causes and consequences of periodic trading activities through a game-theoretic perspective, examining market interactions among different types of participants. Specifically, we introduce a new mean-field liquidation game involving major and minor traders, where the major trader evaluates her strategy against a periodic targeting strategy while a continuum of minor players trade against her. We establish the existence and uniqueness of an open-loop Nash equilibrium. In addition, we prove an O(1/sqrt N) approximation rate of the mean-field solution to the Nash equilibrium in a major-minor game with N minor players. In equilibrium, minor traders exhibit front-running behaviors in both the periodic and trend components of their strategies, reducing the major trader's profit. Such strategic interactions diminish the strength of periodicity in both overall trading volume and asset prices. Our model rationalizes observed periodic trading activities in the market and offers new insights into market dynamics. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.09505 |
| By: | Kshama Dwarakanath; Svitlana Vyetrenko; Tucker Balch |
| Abstract: | We present an agent-based simulator for economic systems with heterogeneous households, firms, central bank, and government agents. These agents interact to define production, consumption, and monetary flow. Each agent type has distinct objectives, such as households seeking utility from consumption and the central bank targeting inflation and production. We define this multi-agent economic system using an OpenAI Gym-style environment, enabling agents to optimize their objectives through reinforcement learning. Standard multi-agent reinforcement learning (MARL) schemes, like independent learning, enable agents to learn concurrently but do not address whether the resulting strategies are at equilibrium. This study integrates the Policy Space Response Oracle (PSRO) algorithm, which has shown superior performance over independent MARL in games with homogeneous agents, with economic agent-based modeling. We use PSRO to develop agent policies approximating Nash equilibria of the empirical economic game, thereby linking to economic equilibria. Our results demonstrate that PSRO strategies achieve lower regret values than independent MARL strategies in our economic system with four agent types. This work aims to bridge artificial intelligence, economics, and empirical game theory towards future research. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.12038 |
| By: | Natalie Kessler (Vrije Universiteit Amsterdam); Iman van Lelyveld (Vrije Universiteit Amsterdam); Ellen van der Woerd (De Nederlandsche Bank) |
| Abstract: | We rationalize exclusive portfolio dealing in a novel three-period partial equilibrium framework populated by a representative, risk-neutral seller and a small number of ex ante identical broker-dealers. Endowed with independent, uncertain demand for a representative asset, the broker-dealers may compete in prices for exclusivity. If no exclusivity is granted, due to either the lack or seller rejection of offers, the seller enters a second-price auction with a zero-loss reserve price. While seller profits are constant under exclusivity (Bertrand Paradox), auction profits increase in the number of broker-dealers. Therefore, exclusivity arises in equilibrium only for a seller with at most two broker-dealers, reducing the trade frequency by one-third. The results are robust to endogenizing the number of broker-dealers and to allowing for the ex post asymmetry in asset demand. Exclusivity, however, does not arise when the auction features a seller-optimal reserve price. We motivate and conclude with an application to the security lending market. |
| Keywords: | Exclusive Dealing, Intermediated Markets, Competition, Market Efficiency |
| JEL: | G14 G24 D43 D86 |
| Date: | 2024–03–20 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240019 |
| By: | Fabian R. Pieroth; Tuomas Sandholm |
| Abstract: | In practice, most auction mechanisms are not strategy-proof, so equilibrium analysis is required to predict bidding behavior. In many auctions, though, an exact equilibrium is not known and one would like to understand whether -- manually or computationally generated -- bidding strategies constitute an approximate equilibrium. We develop a framework and methods for estimating the distance of a strategy profile from equilibrium, based on samples from the prior and either bidding strategies or sample bids. We estimate an agent's utility gain from deviating to strategies from a constructed finite subset of the strategy space. We use PAC-learning to give error bounds, both for independent and interdependent prior distributions. The primary challenge is that one may miss large utility gains by considering only a finite subset of the strategy space. Our work differs from prior research in two critical ways. First, we explore the impact of bidding strategies on altering opponents' perceived prior distributions -- instead of assuming the other agents to bid truthfully. Second, we delve into reasoning with interdependent priors, where the type of one agent may imply a distinct distribution for other agents. Our main contribution lies in establishing sufficient conditions for strategy profiles and a closeness criterion for conditional distributions to ensure that utility gains estimated through our finite subset closely approximate the maximum gains. To our knowledge, ours is the first method to verify approximate equilibrium in any auctions beyond single-item ones. Also, ours is the first sample-based method for approximate equilibrium verification. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.11445 |
| By: | Andrea Canidio; Felix Henneke |
| Abstract: | Blockchain trade intent auctions currently intermediate approximately USD 5 billion monthly. Due to production complementarities, the auction is combinatorial: when multiple trade intents from different traders are auctioned off simultaneously, a bidder (here called solver) can generate additional efficiencies by winning a batch of multiple trade intents. However, unlike other combinatorial auctions studied in the literature, the auction has no numeraire. Fairness is a concern as the efficiencies from batching cannot be easily shared between traders. We formalize this problem and study the most commonly used auction formats: batch auctions and multiple simultaneous auctions. We also propose a novel fair combinatorial auction that combines batch auction and multiple simultaneous auctions: solvers submit individual-trade bids and batched bids, but batched bids are considered only if they are better for all traders relative to the outcome of multiple simultaneous auctions (constructed using the individual-trade bids). We find a trade-off between the fairness guarantees provided by the auction (i.e., the minimum each trader can expect to receive) and the expected value of the assets returned to the traders. Also, the amount that each trader receives in the equilibrium of the fair combinatorial auction may be higher or lower than what they receive in the equilibrium of the simultaneous auctions used as a benchmark for fairness. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.12225 |
| By: | Décamps, Jean-Paul; Mariotti, Thomas; Gensbittel, Fabien |
| Abstract: | We prove the existence of a Markov-perfect equilibrium in randomized stopping times for a model of the war of attrition in which the underlying state variable follows a homogenous linear diffusion. We first prove that the space of Markovian randomized stopping times can be topologized as a compact absolute retract. This in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery [16] to prove our existence theorem. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markovperfect equilibrium. |
| Keywords: | War of Attrition, Markovian Randomized Stopping Time, Markov-Perfect Equilibrium, Fixed-Point Theorem. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129668 |
| By: | Raphael Boleslavsky; Aaron Kolb |
| Abstract: | A sender has a privately known preference over the action chosen by a receiver. The sender would like to influence the receiver's decision by providing information, in the form of a statistical experiment or test. The technology for information production is controlled by a monopolist intermediary, who offers a menu of tests and prices to screen the sender's type, possibly including a "threat" test to punish nonparticipation. We characterize the intermediary's optimal screening menu and the associated distortions, which we show may benefit the receiver. We compare the sale of persuasive information with other forms of influence -- overt bribery and controlling access. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03689 |
| By: | Rim Lahmandi-Ayed (CUT - Centre for Unframed Thinking - ESC [Rennes] - ESC Rennes School of Business); Didier Laussel (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales) |
| Abstract: | div>We study a simple model in which two vertically differentiated firms compete in prices and mass advertising on an initially uninformed market. Consumers differ in their preference for quality.There is an upper bound on prices since consumers cannot spend more on the good than a fixed amount (say, their income). Depending on this income and on the ratio between the advertising cost and quality differential (relative advertising cost), either there is no equilibrium in pure strategies or there exists one of the following three types: (1) an interior equilibrium, where both firms have positive natural markets and charge prices lower than the consumer's income; (2) a constrained interior equilibrium, where both firms have positive natural markets, and the high-quality firm charges the consumer's income or (3) a corner equilibrium, where the low-quality firm has no natural market selling only to uninformed customers. We show that no corner equilibrium exists in which the high-quality firm would have a null natural market. At an equilibrium (whenever there exists one), the high-quality firm always advertises more, charges a higher price and makes a higher profit than the low-quality one. As the relative advertising cost goes to infinity, prices become equal and the advertising intensities converge to zero as well as the profits. Finally, the advertising intensities are, at least globally, increasing with the quality differential. Finally, in all cases, as the advertising parameter cost increases unboundedly, both prices converge increasingly towards the consumer's income. |
| Keywords: | random advertising, advertising cost, vertical differentiation |
| Date: | 2024–03–22 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04678637 |
| By: | Alexandre Arnout (Aix-Marseille University, CNRS, AMSE, Marseille France) |
| Abstract: | I consider an electoral competition model where each candidate is associated with an exogenous initial position from which she can deviate to maximize her vote share, a strategy known as flip-flopping. Citizens have an intrinsic preference for consistent candidates, and abstain due to alienation, i.e. when their utility from their preferred candidate falls below a common exogenous threshold (termed the alienation threshold). I show how the alienation threshold shapes candidates’ flip-flopping strategy. When the alienation threshold is high, i.e. when citizens are reluctant to vote, there is no flip-flopping at equilibrium. When the alienation threshold is low, candidates flip-flop toward the center of the policy space. Surprisingly, I find a positive correlation between flip-flopping and voter turnout at equilibrium, despite voters’ preference for consistent candidates. Finally, I explore alternative models in which candidates’ objective function differs from vote share. I show that electoral competition can lead to polarization when candidates maximize their number of votes. |
| Keywords: | flip-flopping, turnout, electoral competition, alienation, polarization |
| JEL: | D72 C72 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2423 |
| By: | Maria Montero (University of Nottingham); Alex Possajennikov (University of Nottingham); Yuliet Verbel (University of Michigan) |
| Abstract: | This paper studies responsibility attribution for outcomes of collusive bribery. In an experiment, participants labeled as either citizens or public officials can propose a bribery transaction to another participant (labeled as either public official or citizen, respectively), who decides whether to accept the proposal. We then let either the victims of the corrupt transaction or the bystanders of it judge the individual decisions of proposing and accepting. We interpret these judgments as a measure of responsibility attribution. We find that labels (citizen or public official) have a stronger effect than roles (proposer or responder): public officials are consistently regarded as more responsible for corruption than citizens, while those accepting a bribe are regarded as only somewhat more responsible than those proposing it. Further, we find that victims judge corruption decisions more severely than bystanders, although bystanders’ judgments are also consistently negative. In treatments with a neutral context, we find that judgments are less harsh than in the corruption context, bystanders’ judgments are much less harsh than those of victims, and responders are judged more severely than proposers. Our results suggest that people judge corrupt actors in context, more harshly when they are labeled as law enforcers (i.e., public officials), and that unaffected parties (i.e., bystanders) react nearly as negatively to corruption as those directly affected by it (i.e., victims). |
| Keywords: | responsibility attribution; bribery; experiment |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2024-06 |
| By: | Kossi Messanh Agbekponou (SMART - Structures et Marché Agricoles, Ressources et Territoires - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Ilaria Fusacchia (ROMA TRE - Università degli Studi Roma Tre = Roma Tre University) |
| Abstract: | Value creation forms the basis for the construction of global value chains (GVCs) and has received significant scholarly attention, yet the issue of value capture or power distribution along supply chains, "within" industries, is still unresolved. A recent property rights framework (Antr`as and Chor, 2013; Alfaro et al., 2019) highlights how final goods producers exert power over their suppliers to optimally organize their sequential production process. In such an environment, how can suppliers (exporters) act strategically to increase their bargaining power with respect to buyers (importers)? We contribute, theoretically and empirically, to a better understanding of the extent to which the division of surplus in the agri-food sector is affected by manufacturing exporters' position in GVCs. We argue that: (1) further upstream specialization along agri-food GVCs increases bargaining power (the "specialization effect"); (2) expansion along GVCs by importing more upstream inputs and exporting more processed goods also increase bargaining (the "expansion effect"); and (3) the "specialization effect" outweighs the "expansion effect" so that the overall effect is similar to the former. These theoretical hypotheses are tested using firm-level data on French agri-food industries (from French customs and the AMADEUS database) over 2002-2017 period. We build on the bilateral stochastic frontier model to measure the bilateral bargaining power of manufacturers. Following recent approaches in the literature, we identify manufacturers that participate in GVCs with those that jointly import and export, and measure their position in value chains through the level of transformation (upstreamness) of goods they use and produce. Hypotheses (1) and (3) are strongly supported and are mainly driven by product mix upgrade and the reduction of the hol-up problem, while hypothesis (2) is weakly supported and is only due to the high-quality production. |
| Keywords: | Bargaining power, Division of surplus, Global value chains, Upstreamness, Agri-food industry |
| Date: | 2024–03–18 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04666053 |