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on Game Theory |
| By: | Maximilian Andres (University of Potsdam, Berlin School of Economics) |
| Abstract: | The present paper proposes a novel approach for equilibrium selection in the infinitely repeated prisoner’s dilemma where players can communicate before choosing their strategies. This approach yields a critical discount factor that makes different predictions for cooperation than the usually considered sub-game perfect or risk dominance critical discount factors. In laboratory experiments, we find that our factor is useful for predicting cooperation. For payoff changes where the usually considered factors and our factor make different predictions, the observed cooperation is consistent with the predictions based on our factor. |
| Keywords: | cooperation, communication, infinitely repeated game, machine learning |
| JEL: | C73 C92 D83 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:pot:cepadp:75&r=gth |
| By: | Guanxing Fu; Paul P. Hager; Ulrich Horst |
| Abstract: | We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while players with an initially long position are only allowed to sell the stock. Under suitable conditions on the model parameters we show that the games are equivalent to games of timing where the players need to determine the optimal times of market entry and exit. We identify the equilibrium entry and exit times and prove that equilibrium mean-trading rates can be characterized in terms of the solutions to a highly non-linear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium both in the mean-field and the $N$-player game. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.10441&r=gth |
| By: | Masaki Miyashita |
| Abstract: | To what extent can an external observer observing an equilibrium action distribution in an incomplete information game infer the underlying information structure? We investigate this issue in a general linear-quadratic-Gaussian framework. A simple class of canonical information structures is offered and proves rich enough to rationalize any possible equilibrium action distribution that can arise under an arbitrary information structure. We show that the class is parsimonious in the sense that the relevant parameters can be uniquely pinned down by an observed equilibrium outcome, up to some qualifications. Our result implies, for example, that the accuracy of each agent's signal about the state is identified, as measured by how much observing the signal reduces the state variance. Moreover, we show that a canonical information structure characterizes the lower bound on the amount by which each agent's signal can reduce the state variance, across all observationally equivalent information structures. The lower bound is tight, for example, when the actual information structure is uni-dimensional, or when there are no strategic interactions among agents, but in general, there is a gap since agents' strategic motives confound their private information about fundamental and strategic uncertainty. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.11333&r=gth |
| By: | Moez Kilani; André de Palma (Université de Cergy-Pontoise, THEMA) |
| Abstract: | We analyze spatial competition on a circle between firms that have multiple outlets and face quadratic transport costs. The equilibrium is a two-stage Nash game: first, firms decide on their locations and then set their prices. We are able to solve analytically simple multi-outlet cases, but for the general case, we require an algorithm to enumerate all non-isomorphic configurations. While price equilibria are explicit and unique, solving the full two-stage game requires numerical methods. In the location game, we consider two scenarios: either firms cannot jump one outlet over a competitors’ outlet, or firms have the flexibility to locate outlets anywhere on the circle. The solution involves a balance between cannibalization, market protection, and spatial monopoly power. We compare prices, profits, and transport costs for all possible configurations. With flexible locations, the firms’ market areas are contiguous. In this case, surprisingly, each firm acts as a spatial monopoly. If regulations enforce that each firm must set the same price for its outlets, head-to-head competition prevails, leading to decreased profits for the firms but to a better-off situation for consumers. |
| Keywords: | Spatial competition, circle, multi-product oligopoly, price-location equilibria, coin change problem |
| JEL: | L13 R32 R53 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2023-18&r=gth |
| By: | Dirk Bergemann (Yale University); Tibor Heumann (Pontificia Universidad Catolica de Chile); Stephen Morris (Massachusetts Institute of Technology) |
| Abstract: | We characterize the bidders' surplus maximizing information structure in an optimal auction for a single unit good and related extensions to multi-unit and multi-good problems. The bidders seeks to find a balance between participation (and the avoidance of exclusion) and efficiency. The information structure that maximizes the bidders' surplus is given by a generalized Pareto distribution at the center of demand distribution, and displays complete information disclosure at either end of the Pareto distribution. |
| Date: | 2024–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2375r1&r=gth |
| By: | Malachy James Gavan; Antonio Penta; |
| Abstract: | We introduce Safe Implementation, a framework for implementation theory that adds to the standard requirements the restriction that agents’ deviations induce outcomes that are acceptable. Our primitives therefore include both a Social Choice Correspondence, as standard, and an Acceptability Correspondence, each mapping every state of the world to a subset of allocations. This framework generalizes standard notions of implementation, and can accommodate a variety of questions, including robustness with respect to mistakes in play, behavioral considerations, state-dependent feasibility restrictions, limited commitment, etc. We provide results both for general solution concepts and for Nash Equilibrium. For the latter, we identify necessary and sufficient conditions (namely, Comonotonicity and safety-no veto) that restrict the joint behavior of the Social Choice and Acceptability Correspondences, which generalize Maskin’s (1977) conditions. We also show that these conditions are quite permissive in important economic applications, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept. |
| Keywords: | Mechanism Design, Implementation, Robustness, Safe Implementation, Comonotonicity, Safe No-Veto |
| JEL: | C72 D82 |
| URL: | http://d.repec.org/n?u=RePEc:liv:livedp:202401&r=gth |
| By: | Flavio Delbono; Carlo Reggiani |
| Abstract: | We propose a new model of mixed oligopoly where a workers’ cooperative firms competes with a number of profit maximising companies. Building upon a large empirical evidence, we innovate as compared to the traditional literature on the objective function of the cooperative; moreover, its membership is treated as endogenous in the Cournot-Nash equilibrium. We show which factors may be responsible of the degeneration of the workers’ cooperative firms, which occurs when the number of members shrinks with respect to the overall employees. |
| JEL: | L21 L25 P13 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:wp1194&r=gth |
| By: | Dziubiński, M.; Goyal, S.; Zhou, J. |
| Abstract: | We study a model of conflict with multiple battlefields and the possibility of investments spillovers between the battlefields. Results of conflicts at the individual battlefields are determined by the Tullock contest success function based on efforts assigned to a battlefield as well as efforts spilling over from the neighbouring battlefields. We characterize Nash equilibria of this model and uncover a network invariance result: equilibrium payoffs, equilibrium total expenditure, and equilibrium probabilities of winning individual battlefields are independent of the network of spillovers. We show that the network invariance holds for any contest success function that is homogeneous of degree zero and has the no-tie property. We define a network index that characterizes equilibrium efforts assignments of the players. We show that the index satisfies neighbourhood inclusion and can, therefore, be considered a network centrality. |
| Keywords: | Conflict, Investments, Models, Networks |
| Date: | 2024–02–21 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2403&r=gth |
| By: | Gergely Horvath |
| Abstract: | We experimentally study effort provision and network formation in the linear-quadratic game characterized by positive externality and complementarity of effort choices among network neighbors. We compare experimental outcomes to the equilibrium and efficient allocations and study the impact of group size and linking costs. We find that individuals overprovide effort relative to the equilibrium level on the network they form. However, their payoffs are lower than the equilibrium payoffs because they create fewer links than it is optimal which limits the beneficial spillovers of effort provision. Reducing the linking costs does not significantly increase the connectedness of the network and the welfare loss is higher in larger groups. Individuals connect to the highest effort providers in the group and ignore links to relative low effort providers, even if those links would be beneficial to form. This effect explains the lack of links in the network. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.05913&r=gth |
| By: | Yohan Pelosse (Humanities and Social Sciences, Swansea University) |
| Abstract: | A primitive assumption underlying Aumann (1974, 1987) is that all players of a game may correlate their strategies by agreeing on a common single ’public roulette’. A natural extension of this idea is the study of strategies when the assumption of a single randomdevice common to all the players (public roulette) is dropped and (arbitrary) disjoint subsets of players forming a coalition structure are allowed to use independent randomdevices (private roulette) a la Aumann. Undermultiple independent randomdevices, the coalitionsmixed strategies forman equilibrium of the induced non-cooperative game played across the coalitions–the ’partitioned game’–when the profile of such coalitions’ strategies is a profile of correlated equilibria. These correlated equilibria which are themutual joint best responses of the coalitions are called the Nash coalitional correlated equilibria (NCCEs) of the game. The paper identifies various classes of finite and infinite games where there exists a non-empty set of NCCEs lying outside the regular correlated equilibrium distributions of the game. We notably relate the class of NCCEs to the ’coalitional equilibria’ introduced in Ray and Vohra (1997) to construct their ’Equilibrium Binding Agreements’. In a ’coalitional equilibrium’, coalitions’ best responses are defined by Pareto dominance and their existence are not guaranteed in arbitrary games without the use of correlated mixed strategies. We characterize a family of games where the existence of a non-empty set of non-trivial NCCEs is guaranteed to coincide with a subset of coalitional equilibria. Most of our results are based on the characterization of the induced non-cooperative ’partitioned game’ played across the coalitions. |
| JEL: | C72 C92 D83 |
| Date: | 2024–03–17 |
| URL: | http://d.repec.org/n?u=RePEc:swn:wpaper:2024-05&r=gth |
| By: | Yang Cai; Yingkai Li; Jinzhao Wu |
| Abstract: | This paper studies a joint design problem where a seller can design both the signal structures for the agents to learn their values, and the allocation and payment rules for selling the item. In his seminal work, Myerson (1981) shows how to design the optimal auction with exogenous signals. We show that the problem becomes NP-hard when the seller also has the ability to design the signal structures. Our main result is a polynomial-time approximation scheme (PTAS) for computing the optimal joint design with at most an $\epsilon$ multiplicative loss in expected revenue. Moreover, we show that in our joint design problem, the seller can significantly reduce the information rent of the agents by providing partial information, which ensures a revenue that is at least $1 - \frac{1}{e}$ of the optimal welfare for all valuation distributions. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08145&r=gth |
| By: | Martino Banchio; Aranyak Mehta; Andres Perlroth |
| Abstract: | We study the design of auctions with dynamic scoring, which allocate a single item according to a given scoring rule. We are motivated by online advertising auctions when users interact with a platform over the course of a session. The platform ranks ads based on a combination of bids and quality scores, and updates the quality scores throughout the session based on the user's online activity. The platform must decide when to show an ad during the session. By delaying the auction, the auctioneer acquires information about an ad's quality, improving her chances of selecting a high quality ad. However information is costly, because delay reduces market thickness and in turn revenue. When should the auctioneer allocate the impression to balance these forces? We develop a theoretical model to study the effect of market design on the trade-off between market thickness and information. In particular, we focus on first- and second-price auctions. The auctioneer can commit to the auction format, but not to its timing: her decision can thus be cast as a real options problem. We show that under optimal stopping the first-price auction allocates efficiently but with delay. Instead, the second-price auction generates more revenue by avoiding delay. The auctioneer benefits from introducing reserve prices, more so in a first-price auction. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.11022&r=gth |
| By: | Tomiyama, Hideyuki; Otsu, Taisuke |
| Abstract: | By extending de Paula and Tang (2012) and Aradillas-López and Gandhi (2016), we derive testable restrictions for uniqueness of equilibrium in games with multi-dimensional actions. We discuss two models of payoff functions which imply certain covariance restrictions for players’ actions. These restrictions can be used to construct an identified set of strategic parameters under multiple equilibria. |
| Keywords: | multiple equilibria; partial identification; moment inequalities |
| JEL: | C14 |
| Date: | 2022–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:114341&r=gth |
| By: | Stephan Lauermann; Asher Wolinsky |
| Abstract: | Auction models are convenient abstractions of informal price formation processes that arise in markets for assets or services. These processes involve frictions such as bidder recruitment costs for sellers, participation costs for bidders, and limitations on sellers commitment abilities. This paper develops an auction model that captures such frictions. We derive several novel predictions; in particular, we find that outcomes are often inefficient, and the market sometimes unravels. |
| Keywords: | Auctions |
| JEL: | D44 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_519&r=gth |
| By: | Qirui Mi; Zhiyu Zhao; Siyu Xia; Yan Song; Jun Wang; Haifeng Zhang |
| Abstract: | Effective macroeconomic policies play a crucial role in promoting economic growth and social stability. This paper models the optimal macroeconomic policy problem based on the \textit{Stackelberg Mean Field Game} (SMFG), where the government acts as the leader in policy-making, and large-scale households dynamically respond as followers. This modeling method captures the asymmetric dynamic game between the government and large-scale households, and interpretably evaluates the effects of macroeconomic policies based on microfoundations, which is difficult for existing methods to achieve. We also propose a solution for SMFGs, incorporating pre-training on real data and a model-free \textit{Stackelberg mean-field reinforcement learning }(SMFRL) algorithm, which operates independently of prior environmental knowledge and transitions. Our experimental results showcase the superiority of the SMFG method over other economic policies in terms of performance, efficiency-equity tradeoff, and SMFG assumption analysis. This paper significantly contributes to the domain of AI for economics by providing a powerful tool for modeling and solving optimal macroeconomic policies. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.12093&r=gth |
| By: | Ohnishi, Kazuhiro |
| Abstract: | Nonpoint pollution arises from dispersed sources and lacks direct monitoring. Observing individual abatement levels or discharges is generally impractical. This paper addresses the economic incentives for controlling nonpoint pollution, which differs from point source pollution due to difficulties in monitoring individual polluting actions. The paper examines a mixed Bertrand duopoly model where there are two firms: a private firm and a partially privatized public firm that is jointly owned by the public and private sectors. The model of the paper uses ambient charges as a policy measure for reducing industrial nonpoint source pollution. This paper shows that ambient charges are an effective policy measure. |
| Keywords: | Ambient charge; Nonpoint pollution: Partial privatization; Price competition |
| JEL: | D21 L33 Q58 |
| Date: | 2024–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120531&r=gth |
| By: | Hans Gersbach; Fikri Pitsuwan; Giovanni Valvassori Bolgè |
| Abstract: | We examine democratic public-good provision with heterogeneous legislators. Decisions are taken by majority rule and an agenda-setter proposes a level of the public good, taxes, and subsidies. Members are heterogeneous with respect to their benefits from the public good. We find that, depending on the status quo public-good level, the agenda-setter will form a coalition with the agents who most desire, or least desire, the public good, and we may observe ‘strange bedfellow’ coalitions. Moreover, public-good provision is a non-monotonic function of the status quo public-good level. In the dynamic setting, public-good provision fluctuates endogenously, even if the agenda-setter stays the same over time. Moreover, the more polarized the legislature is, the higher is the volatility of public-good provision and the longer it may take for a society to recover from negative shocks to public-good provision. We illustrate these findings for a two-party system with polarized parties. |
| Keywords: | legislative bargaining, coalition, public goods, polarization, resilience |
| JEL: | C73 D72 H50 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_11004&r=gth |
| By: | Choi, S.; Goyal, S.; Guo, F.; Moisan, F. |
| Abstract: | Social interactions shape individual behavior and public policy increasingly uses networks to improve effectiveness. It is therefore important to understand if the theoretical predictions on the relation between networks and individual choice are empirically valid. This paper tests a key result in the theory of games on networks: an individual’s action is proportional to their (Bonacich) centrality. Our experiment shows that individual efforts increase in centrality but at a rate of increase that is lower than the theoretical prediction. These departures from equilibrium are accompanied by significant departures in individual earnings from theoretical predictions. We propose a model of network based imitation decision rule to explain these deviations. |
| JEL: | C92 D83 D85 Z13 |
| Date: | 2024–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2401&r=gth |
| By: | Inkoo Cho; Noah Williams |
| Abstract: | We develop a model of algorithmic pricing that shuts down every channel for explicit or implicit collusion while still generating collusive outcomes. We analyze the dynamics of a duopoly market where both firms use pricing algorithms consisting of a parameterized family of model specifications. The firms update both the parameters and the weights on models to adapt endogenously to market outcomes. We show that the market experiences recurrent episodes where both firms set prices at collusive levels. We analytically characterize the dynamics of the model, using large deviation theory to explain the recurrent episodes of collusive outcomes. Our results show that collusive outcomes may be a recurrent feature of algorithmic environments with complementarities and endogenous adaptation, providing a challenge for competition policy. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.07177&r=gth |
| By: | S. Nobili |
| Abstract: | Over the past few decades, there has been a notable increase in firms' market power accompanied by a global decrease in Corporate Income Tax (CIT) rates. This paper provides a theoretical framework to shed light on these diverging trends. I develop a general equilibrium model that incorporates imperfect competition and strategic interaction among firms, allowing them to shift profits abroad towards a tax haven. I find that increasing firms' market power enhances their incentives to engage in profit shifting, via larger profits. Profits rise through (i) larger markdowns and (ii) reallocation of market share towards more productive firms. A government, competing to retain firms' profits, set low tax rates to prevent local firms from evading toward tax haven(s). The competition is stronger, i.e. lower tax rates, when firms' market power is higher. Besides, I find that profit shifting widens the disparities among ex-ante heterogeneous firms and endogenously increases the level of market power in the economy, favouring the most productive firms. |
| Keywords: | L13;H73;H25;F23;E61;D43 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:cns:cnscwp:202406&r=gth |
| By: | Juan Carlos Gon\c{c}alves-Dosantos; Ricardo Mart\'inez; Joaqu\'in S\'anchez-Soriano |
| Abstract: | Digital streaming platforms, including Twitch, Spotify, Netflix, Disney, and Kindle, have emerged as one of the main sources of entertainment with significant growth potential. Many of these platforms distribute royalties among streamers, artists, producers, or writers based on their impact. In this paper, we measure the relevance of each of these contributors to the overall success of the platform, which is information that can play a key role in revenue allocation. We perform an axiomatic analysis to provide normative foundations for three relevance metrics: the uniform, the proportional, and the subscriber-proportional indicators. The last two indicators implement the so-called pro-rata and user-centric models, which are extensively applied to distribute revenues in the music streaming market. The axioms we propose formalize different principles of fairness, stability, and non-manipulability, and are tailor-made for the streaming context. We complete our analysis with a case study that measures the influence of the 19 most-followed streamers worldwide on the Twitch platform. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08421&r=gth |
| By: | Laszlo Goerke (Institute for Labour Law and Industrial Relations in the European Union (IAAEU), Trier University); Nora Paulus (University of Luxembourg) |
| Abstract: | If a profit-maximising firm credibly commits to an employment-enhancing Corporate Social Responsibility (CSR) objective in negotiations with a trade union, the union can reduce its wage demands. Lower wages, ceteris paribus, raise profits, while the increase in employment enhances the payoff of a wage-setting trade union. Therefore, both the firm and the trade union can be better off in the presence of a collectively bargained CSR-objective than in its absence. Accordingly, establishing a CSR-objective can give rise to a Pareto-improvement and can mitigate the inefficiency resulting from collective wage negotiations. |
| Keywords: | : Collective Bargaining, Corporate Social Responsibility, Employment, Pareto-Improvement, Trade Union, Wages |
| JEL: | D60 J51 M14 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:iaa:dpaper:202401&r=gth |
| By: | Mella-Barral, P.; Sabourian, H. |
| Abstract: | Firms can voluntarily create independent firms to implement their technologically distant innovations and capture their value through capital markets. We argue that when firms repeatedly compete to make innovations, there is inefficient external implementation of innovations and “excessive†creation of such firms. This inefficiency is most exacerbated in the early stages of an industry, when the number of firms is still limited. |
| Keywords: | Repeated Innovations, Spin-Offs, Voluntary Firm Creation |
| JEL: | M13 O31 O33 |
| Date: | 2023–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2312&r=gth |