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on Game Theory |
| By: | Florian Herold; Christoph Kuzmics |
| Abstract: | In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle with this column vector. We use Farkas' lemma to show that this player can be made indifferent between all pure strategies if and only if the union of all these half spaces covers the whole vector space. This result leads to a necessary (and almost sufficient) condition for a game to have a completely mixed Nash equilibrium. We demonstrate its usefulness by providing the class of all symmetric two player three strategy games that have a unique and completely mixed symmetric Nash equilibrium. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02620&r=gth |
| By: | Malte Baader (University of Zurich); Simon Gächter (University of Nottingham); Kyeongtae Lee (Bank of Korea); Martin Sefton (University of Nottingham) |
| Abstract: | We experimentally examine how incentives affect conditional cooperation (i.e., cooperating in response to cooperation and defecting in response to defection) in social dilemmas. In our first study, subjects play eight Sequential Prisoner’s Dilemma games with varying payoffs. We elicit second mover strategies and find that most second movers conditionally cooperate in some games and free ride in others. The rate of conditional cooperation is higher when the own gain from defecting is lower and when the loss imposed on the first mover by defecting is higher. This pattern is consistent with both social preference models and stochastic choice models. In a second study subjects play 64 social dilemma games, and we jointly estimate noise and social preference parameters at the individual level. Most of our subjects place significantly positive weight on others’ payoffs, supporting the underlying role of social preferences in conditional cooperation. Our results suggest that conditional cooperation is not a fixed trait but rather a symptom of the interaction between game incentives and underlying social preferences. |
| Keywords: | sequential prisoner’s dilemma; conditional cooperation; social preferences |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2024-04&r=gth |
| By: | Davide Bosco (University of Milan-Bicocca and Center for European Studies); Luca Portoghese (University of Pavia) |
| Abstract: | This paper studies how private information about health states affects social distancing behaviour in epidemics. We propose a social-interaction game where agents are rational and demographically heterogeneous, and the risk of death post-infection depends on demography. Self-tests and public screening campaigns jointly determine the available information. We find that private information determines how the spatial characteristics of the social environment affect agents’ strategic interplay: if private information is not available, social distancing decisions are strategic substitutes in any environment; if private information is available, complementarity arises in congestionable environments, and substitutability prevails otherwise. Policy implications ensue: if self-tests that detect illness are freely available, mass screening campaigns with tests that detect recoveries are beneficial in congestionable environments, but increase the death toll in the absence of congestion. |
| Keywords: | COVID-19, Contagion, Social distancing, Collective action, Strategic complements and substitutes |
| JEL: | C72 D71 H41 I13 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:pav:demwpp:demwp0218&r=gth |
| By: | Yuliyan Mitkov (University of Bonn) |
| Abstract: | I endogenize the probability of self-fulfilling outcomes in a game where the only uncertainty comes from extrinsic sunspots. There is a group of players wishing to coordinate on the same action and another player, the regime defender, whose action affects the payoff from coordination. The coordinating players’ actions can be based on a sunspot state, which, unlike in the classic sunspot approach, is observed with a small, idiosyncratic noise (a private sunspot). I show how private sunspots, combined with the action of the regime defender, can be used to derive a unique coordination probability in any equilibrium where sunspots influence actions. I show how this approach can be used to determine the probability of a sunspot-driven bank run. |
| Keywords: | Coordination problems, sunspots, strategic uncertainty |
| JEL: | D70 D84 G01 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:295&r=gth |
| By: | Luca Anderlini (Georgetown University, University of Naples Federico II and CSEF); Gaon Kim (EIEF and LUISS University) |
| Abstract: | We examine “tournament” second-price auctions in which N bidders compete for the right to participate in a second stage and contend against bidder N +1. When the first N bidders are committed so that their bids cannot be changed in the second stage, the analysis yields some unexpected results. The first N bidders consistently bid above their values in equilibrium. When bidder N + 1 is sufficiently stronger than the first N, overbidding leads to an increase in expected revenue in comparison to the standard second-price auction when N is large. |
| Keywords: | Tournament Auctions, Overbidding, Revenue Equivalence. |
| JEL: | C70 C72 C79 |
| Date: | 2024–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:712&r=gth |
| By: | Maxim Senkov; Toygar T. Kerman |
| Abstract: | We study a Bayesian persuasion model with two-dimensional states of the world, in which the sender (she) and receiver (he) have heterogeneous prior beliefs and care about different dimensions. The receiver is a naive agent who has a simplistic worldview: he ignores the dependency between the two dimensions of the state. We provide a characterization for the sender’s gain from persuasion both when the receiver is naive and when he is rational. We show that the receiver benefits from having a simplistic worldview if and only if it makes him perceive the states in which his interest is aligned with the sender as less likely. |
| Keywords: | Bayesian persuasion, misspecified prior, correlation neglect |
| JEL: | D82 D83 D91 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp773&r=gth |
| By: | Toygar T. Kerman; Anastas P. Tenev |
| Abstract: | We study a multiple-receiver Bayesian persuasion model in which the sender wants to achieve an outcome and commits to an experiment which sends correlated messages to homogeneous receivers. Receivers are connected in a network and can perfectly observe their immediate neighbors’ messages. After updating their beliefs, receivers choose an action to match the true state of the world. Surprisingly, the sender’s gain from persuasion does not change monotonically with network density. We characterize a class of networks in which increased communication among the receivers is strictly better for the sender and hence strictly worse for the receivers. |
| Keywords: | Bayesian Persuasion, Networks, Critical Mass, Voting |
| JEL: | C72 D72 D82 D85 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp772&r=gth |
| By: | Shanglyu Deng; Dun Jia; Mario Leccese; Andrew Sweeting |
| Abstract: | Industries with significant scale economies or learning-by-doing may come to be dominated by a single firm. Economists have studied how likely this is to happen, and whether it is efficient, using models where buyers are price or quantity takers, even though these industries are often also characterized by buyer-seller negotiations. We extend the dynamic “learning-by-doing and forgetting” model of Besanko, Doraszelski, Kryukov, and Satterthwaite (2010) to allow for Nash-in-Nash bargaining over prices. Price-taking and the social planner solution are captured as special cases. We show that sellers’ dynamic incentives, market concentration and welfare can change sharply, and non-monotonically, as one moves away from the price-taking assumption. We study the implications of buyer bargaining power for the existence of multiple equilibria, the design of subsidy policies and the welfare effects of policies designed to increase competition. |
| JEL: | C73 D21 D43 L13 L41 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32360&r=gth |
| By: | Francesc Dilme (Department of Economics, University of Bonn) |
| Abstract: | This paper studies repeated trade with noisy information about previous transactions. A buyer has private informa- tion about his willingness to pay, which is either low or high, and buys goods from different sellers over time. Each seller observes a noisy history of signals about the buyer’s previous purchases and sets a price. We compare the cases where previous prices are observable to sellers with the case where they are not. We show that more signal precision is counterbalanced by two equilibrium mechanisms that slow learning and keep incentives in balance: (1) sellers offer discounted prices more often, and (2) the buyer rejects high prices with a higher probability. The effect of making prices observable depends on the signal precision: When the signal is imprecise, making prices public strengthens the discounting mechanism, improving efficiency and buyer welfare; when the signal is precise, making prices public activates the rejection mechanism, and efficiency and buyer welfare may decrease. Independently of the price observability, the buyer tends to benefit from a more precise signal about previous purchases. |
| Keywords: | Repeated trade, asymmetric information, internet cookies |
| JEL: | C73 C78 D82 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:296&r=gth |
| By: | Byung-Cheol Kim (University of Alabama); Jin Yeub Kim (Yonsei University); Hyunjun Cho (Yonsei University) |
| Abstract: | In a partnership game, a principal and an agent negotiate over their profitsharing rule, after which each individually chooses effort, generating profits. We study the roles of complementarity in efforts, asymmetric productivity, and timing of effort choices in profit-sharing partnerships. When the agent is relatively more productive than the principal, the agent gets lower bargaining power under a stronger degree of complementarity. The surplus of the partnership is always higher in the case of sequential effort choice than in the simultaneous-choice counterpart. We provide implications for allocation of ownership in corporate governance, surplus maximization in partnerships, and optimal hiring. |
| Keywords: | game theory; Partnership, Ownership Structure, Profit-Sharing Rule, Negotiation, Complementarity. |
| JEL: | C72 C78 G32 L14 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2024rwp-224&r=gth |
| By: | Erhan Bayraktar; Asaf Cohen; April Nellis |
| Abstract: | We investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the prices of assets in the wider market. They engage in a game among themselves, and the resulting liquidity distribution determines the exchange rate dynamics and potential arbitrage opportunities of the pool. We calibrate the distribution of LP characteristics based on Uniswap data and the equilibrium strategy resulting from this mean-field game produces pool exchange rate dynamics and liquidity evolution consistent with observed pool behavior. We subsequently introduce Maximal Extractable Value (MEV) bots who perform Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between LPs and bots. This addition results in more accurate simulated pool exchange rate dynamics and stronger predictive power regarding the evolution of the pool liquidity distribution. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.09090&r=gth |
| By: | Patrick Rey; Yossi Spiegel; Konrad Stahl |
| Abstract: | We study the feasibility and profitability of predtion in a dynamic environment, using a parsimonious infinite-horizon, complete information setting in which an incumbent repeatedly faces potential entry. When a rival enters, the incumbent chooses whether to accommodate or predate it; the entrant then decides whether to stay or exit. We show that there always exists a Markov perfect equilibrium, which can be of three types: accommodation, monopolization, and recurrent predation. We then analyze and compare the welfare effects of different antitrust policies, accounting for the possibility that recurrent predtion may be welfare improving. |
| Keywords: | predation, accommodation, entry, legal rules, Markov perfect equilibrium |
| JEL: | D43 L41 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_529&r=gth |
| By: | Luca Anderlini (Georgetown University, University of Naples Federico II and CSEF); Larry Samuelson (Yale University); Daniele Terlizzese (EIEF) |
| Abstract: | We examine an economy in which interactions are more productive if agents can trust others to refrain from cheating. Some agents are scoundrels, who always cheat, while others cheat only if the cost of cheating, a decreasing function of the proportion of cheaters, is sufficiently low. The economy exhibits multiple equilibria. As the proportion of scoundrels in the economy declines, the high-trust equilibrium can be disrupted by arbitrarily small perturbations or infusions of low-trust agents, while the low-trust equilibrium becomes impervious to perturbations and infusions of high-trust agents. The resilience of trust may thus hinge upon the prevalence of scoundrels. |
| Keywords: | Trust, Robustness, Fragility, Assimilation, Disruption. |
| JEL: | C72 C79 D02 D80 |
| Date: | 2024–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:710&r=gth |
| By: | Michail Anthropelos; Scott Robertson |
| Abstract: | We consider a market of risky financial assets where the participants are an informed trader, a mass of uniformed traders and noisy liquidity providers. We prove the existence of a market-clearing equilibrium when the insider internalizes her power to impact prices. In the price-impact equilibrium the insider strategically reveals a noisier (compared to when the insider takes prices as given) signal, and prices are less reactive to the publicly available information. In contrast to the related literature, we show that in the price-impact equilibrium, the insider's ex-ante welfare monotonically increases in the signal precision. This clarifies when a trader with market power is motivated to both obtain and refine her private information. Furthermore, even though the uniformed traders act as price-takers, the effect of price impact is ex-ante welfare improving for them. By contrast, internalization of price impact may reduce insider ex-ante welfare. This happens provided the insider is sufficiently risk averse and the uninformed traders are sufficiently risk tolerant. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.08757&r=gth |
| By: | Shaomin Wu |
| Abstract: | In this paper, I characterize the network formation process as a static game of incomplete information, where the latent payoff of forming a link between two individuals depends on the structure of the network, as well as private information on agents' attributes. I allow agents' private unobserved attributes to be correlated with observed attributes through individual fixed effects. Using data from a single large network, I propose a two-step estimator for the model primitives. In the first step, I estimate agents' equilibrium beliefs of other people's choice probabilities. In the second step, I plug in the first-step estimator to the conditional choice probability expression and estimate the model parameters and the unobserved individual fixed effects together using Joint MLE. Assuming that the observed attributes are discrete, I showed that the first step estimator is uniformly consistent with rate $N^{-1/4}$, where $N$ is the total number of linking proposals. I also show that the second-step estimator converges asymptotically to a normal distribution at the same rate. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.12581&r=gth |
| By: | Matteo Bizzarri (University of Naples Federico II and CSEF.); Fernando Vega-Redondo (Bocconi University and BIDSA.) |
| Abstract: | We characterize the firm-level welfare effects of a small change in ownership overlap, and how it depends on the position in the production network. In our model, firms compete in prices, internalizing how their decisions affect the firms lying downstream as well as those that have common shareholders. While in a horizontal economy the common-ownership effects on equilibrium prices depend on firm markups alone, in the more general case displaying vertical inter-firm relationships a full knowledge of the production network is typically required. Addressing then the normative question of what are the welfare implications of affecting the ownership structure, we show that, if costs of adjusting it are large, the optimal intervention is proportional to the Bonacich centrality of each firm in the weighted network quantifying interfirm price-mediated externalities. Finally, we also explain that the parameters of the model can be identified from typically available data, hence rendering our model amenable to empirical analysis. |
| Keywords: | production networks, network games, common ownership, oligopoly. |
| JEL: | D43 D57 D85 L13 L16 |
| Date: | 2024–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:707&r=gth |
| By: | Andreas Hauer (Seminar for Economic Policy, LMU); Hayato Kato (Graduate School of Economics, Osaka University) |
| Abstract: | The Global Minimum Tax (GMT) is applied only to firms above a certain size threshold. We set up a simple model of tax competition and profit shifting by heterogeneous multinational firms to evaluate the e ects of this partial coverage of the GMT. A non-haven and a haven country are bound by the GMT rate for large multinationals, but can set tax rates for firms below the threshold non-cooperatively. We show that the introduction of the GMT with a moderate tax rate increases tax revenues in both the non-haven and the haven countries. Gradual increases in the GMT rate, however, trigger a sudden change in the tax competition equilibrium from a uniform to a split corporate tax rate, at which tax revenues in the non-haven country decline. In contrast, gradual increases in the coverage of the GMT never harm the non-haven country. We also discuss the quantitative e ects of introducing a 15% GMT rate in a calibrated version of our model. |
| Keywords: | multinational firms; tax avoidance; profit shifting; tax competitionInput-output |
| JEL: | F23 H25 H87 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:2406&r=gth |
| By: | Luca Anderlini (Georgetown University, University of Naples Federico II and CSEF); Leonardo Felli (University of Cambridge); Michele Piccione (London School of Economics.) |
| Abstract: | How do mechanisms that enforce cooperation emerge in a society where none are available and agents are endowed with raw power, that allows a more powerful agent to expropriate a less powerful one? We study a model where expropriation is costly and agents can choose whether to engage in surplus-augmenting cooperation or engage in expropriation. While in bilateral relations, if cooperation is not overwhelmingly productive and expropriation is not too costly, the latter will prevent cooperation, when there are three or more agents, powerful ones can become enforcers of cooperation for agents ranked below them. In equilibrium they will expropriate smaller amounts from multiple weaker cooperating agents who in turn will not deviate for fear of being expropriated more heavily because of their larger expropriation proceeds. Surprisingly, the details of the power structure are irrelevant for the existence of equilibria with enforcement provided that enough agents are present and one is ranked above all others. These details are instead key to the existence of other highly noncooperative equilibria that obtain in certain cases. |
| Keywords: | Jungle, Power Structures, Enforcement, Rule of Law. |
| JEL: | C79 D00 D01 D31 K19 K40 K49 |
| Date: | 2024–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:711&r=gth |
| By: | Liu, Kaiqi (RS: GSBE UM-BIC, Microeconomics & Public Economics); Rusch, Hannes (RS: GSBE UM-BIC, Microeconomics & Public Economics, RS: GSBE other - not theme-related research); Seel, Christian (RS: GSBE other - not theme-related research, Microeconomics & Public Economics); Terstiege, Stefan (RS: GSBE UM-BIC, Microeconomics & Public Economics) |
| Abstract: | We model student enrollment in markets for higher education where public universities, private non-profit universities, and private for-profit universities compete. Universities differ with respect to their capacity, graduation probability, and profit objective; students differ in ability. The value of a diploma at each university depends on its endogenous ranking based on average student ability. In every equilibrium, the private for-profit university attracts the least able students. Under additional conditions, the private non-profit university attracts the top students. Paradoxically, a higher capacity at the public university might decrease its equilibrium market share as it incentivizes the for-profit university to compete more aggressively. The for-profit university benefits from an increased enrollment in higher education. |
| JEL: | C78 I23 |
| Date: | 2024–04–18 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2024005&r=gth |