
on Game Theory 
By:  Ata Atay (Department of Mathematical Economics, Finance and Actuarial Sciences, and Barcelona Economic Analysis Team (BEAT), University of Barcelona, Spain); Christian Trudeau (Department of Economics, University of Windsor) 
Abstract:  Cooperative game theory aims to study how to divide a joint value created by a set of players. These games are often studied through the characteristic function form with transferable utility, which represents the value obtainable by each coalition. In the presence of externalities, there are many ways to define this value. Various models that account for different levels of player cooperation and the influence of external players on coalition value have been studied. Although there are different approaches, typically, the optimistic and pessimistic approaches provide sufficient insights into strategic interactions. This paper clarifies the interpretation of these approaches by providing a unified framework. We show that making sure that no coalition receives more than their (optimistic) upper bounds is always at least as difficult as guaranteeing their (pessimistic) lower bounds. We also show that if externalities are negative, providing these guarantees is always feasible. Then, we explore applications and show how our findings can be applied to derive results from the existing literature. 
Keywords:  Cooperative games, optimization problems, cost sharing, core, anticore, externalities. 
JEL:  C44 C71 D61 D62 D63 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:wis:wpaper:2401&r=gth 
By:  Edith Elkind; Abheek Ghosh; Paul W. Goldberg 
Abstract:  Tullock contests model reallife scenarios that range from competition among proofofwork blockchain miners to rentseeking and lobbying activities. We show that continuoustime bestresponse dynamics in Tullock contests with convex costs converges to the unique equilibrium using Lyapunovstyle arguments. We then use this result to provide an algorithm for computing an approximate equilibrium. We also establish convergence of related discretetime dynamics, e.g., when the agents bestrespond to the empirical average action of other agents. These results indicate that the equilibrium is a reliable predictor of the agents' behavior in these games. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.08541&r=gth 
By:  Justin Chan 
Abstract:  Cooperative games can be distinguished as noncooperative games in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When the payoffs to each coalition under some noncooperative solution concept coincide with their value in the cooperative game, the cooperative game is said to be implementable and the noncooperative game its implementation. This paper proves that all strictly superadditive partition function form games are implementable under Nash equilibrium and rationalizability; that all weakly superadditive characteristic function form games are implementable under Nash equilibrium; and that all weakly superadditive partition function form games are implementable under trembling hand perfect equilibrium. Discussion then proceeds on the appropriate choice of noncooperative solution concept for the implementation. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.14952&r=gth 
By:  Mika Sutela; Nino Lindstr\"om 
Abstract:  We expand on earlier research on the topic by discussing an infinitely repeated game model with a subgame perfect equilibrium strategy profile (SPE) as a solution concept that diminishes incentives to violate speed limits in a carrot and stick fashion. In attempts to construct an SPE strategy profile, the initial state is chosen such that the drivers are playing a mixed strategy whereas the police is not enforcing with certainty. We also postulate a short period version of the repeated game with generalized stage game payoffs. For this game, we construct a multistage strategy profile that is a Nash equilibrium but not an SPE. Some solution candidates are excluded by showing that they do not satisfy a one shot deviation property that is a necessary condition for an SPE profile in a repeated game of perfect information. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.09556&r=gth 
By:  Abhimanyu Nag; Samrat Gupta; Sudipan Sinha; Arka Datta 
Abstract:  Decentralized Finance (DeFi) ecosystems, exemplified by the Maker Protocol, rely on intricate games to maintain stability and security. Understanding the dynamics of these games is crucial for ensuring the robustness of the system. This motivating research proposes a novel methodology leveraging MultiAgent Influence Diagrams (MAID), originally proposed by Koller and Milch, to dissect and analyze the games within the Maker stablecoin protocol. By representing users and governance of the Maker protocol as agents and their interactions as edges in a graph, we capture the complex network of influences governing agent behaviors. Furthermore in the upcoming papers, we will show a Nash Equilibrium model to elucidate strategies that promote coordination and enhance economic security within the ecosystem. Through this approach, we aim to motivate the use of this method to introduce a new method of formal verification of game theoretic security in DeFi platforms. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.15037&r=gth 
By:  Elliot Lipnowski; Doron Ravid; Denis Shishkin 
Abstract:  A sender commits to an experiment to persuade a receiver. Accounting for the sender's experimentchoice incentives, and not presupposing a receiver tiebreaking rule when indifferent, we characterize when the sender's equilibrium payoff is unique and so coincides with her "Bayesian persuasion" value. A sufficient condition in finite models is that every action which is receiveroptimal at some belief is uniquely optimal at some other belief  a generic property. We similarly show the equilibrium sender payoff is typically unique in ordered models. In an extension, we show uniqueness generates robustness to imperfect sender commitment. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.06765&r=gth 
By:  Lina Lozano; Arno Riedl; Christina Rott 
Abstract:  We investigate experimentally how the menstrual cycle affects bargaining behavior and bargaining outcomes of women. Female participants negotiate in an unstructured bilateral bargaining game with asymmetric information about the allocation of a surplus (’pie size’). We find that the menstrual cycle affects bargaining behavior and that the effects depend on the information players have. Players who are informed about the pie size are less compromising during ovulation and receive higher payoffs conditional on reaching an agreement. Uninformed players achieve higher final payoffs during ovulation, which is mainly driven by higher agreement rates. 
Keywords:  bargaining, asymmetric information, menstrual cycle, biological factors 
JEL:  C78 C91 D87 J16 
Date:  2024 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_10932&r=gth 
By:  Siyang Xiong 
Abstract:  Traditionally, mechanism design focuses on simultaneousmove games (e.g., Myerson (1981)). In this paper, we study mechanism design with sequentialmove games, and provide two results on revelation principles for general solution concepts (e.g., perfect Bayesian equilibrium, obvious dominance, strongobvious dominance). First, if a solution concept is additive, implementation in sequentialmove games is equivalent to implementation in simultaneousmove games. Second, for any solution concept \r{ho} and any social choice function f, we identify a canonical operator {\gamma}^{(\r{ho}, f)}, which is defined on primitives. We prove that, if \r{ho} is monotonic, f can be implemented by a sequentialmove game if and only if {\gamma}^{(\r{ho}, f)} is achievable, which translates a complicated mechanism design problem into checking some conditions defined on primitives. Most of the existing solution concepts are either additive or monotonic. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.13580&r=gth 
By:  Devansh Jalota; Michael Ostrovsky; Marco Pavone 
Abstract:  Fraudulent or illegal activities are ubiquitous across applications and involve users bypassing the rule of law, often with the strategic aim of obtaining some benefit that would otherwise be unattainable within the bounds of lawful conduct. However, user fraud is detrimental, as it may compromise safety or impose disproportionate negative externalities on particular population groups. To mitigate the potential harms of user fraud, we study the problem of policing such fraud as a security game between an administrator and users. In this game, an administrator deploys $R$ security resources (e.g., police officers) across $L$ locations and levies fines against users engaging in fraud at those locations. For this security game, we study both welfare and revenue maximization administrator objectives. In both settings, we show that computing the optimal administrator strategy is NPhard and develop natural greedy algorithm variants for the respective settings that achieve at least half the welfare or revenue as the welfaremaximizing or revenuemaximizing solutions, respectively. We also establish a resource augmentation guarantee that our proposed greedy algorithms with one extra resource, i.e., $R+1$ resources, achieve at least the same welfare (revenue) as the welfaremaximizing (revenuemaximizing) outcome with $R$ resources. Finally, since the welfare and revenuemaximizing solutions can differ significantly, we present a framework inspired by contract theory, wherein a revenuemaximizing administrator is compensated through contracts for the welfare it contributes. Beyond extending our theoretical results in the welfare and revenue maximization settings to studying equilibrium strategies in the contract game, we also present numerical experiments highlighting the efficacy of contracts in bridging the gap between the revenue and welfaremaximizing administrator outcomes. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.11209&r=gth 
By:  Vijay V. Vazirani 
Abstract:  The set of core imputations of the assignment game forms a (nonfinite) distributive lattice. So far, efficient algorithms were known for computing only its two extreme imputations; however, each of them maximally favors one side and disfavors the other side of the bipartition, leading to inequitable profit sharing. Another issue is that a subcoalition consisting of one player (or a set of players from the same side of the bipartition) can make zero profit, therefore a core imputation is not obliged to give them any profit. Hence core imputations make no fairness guarantee at the level of individual agents. This raises the question of computing {\em more equitable core imputations}. In this paper, we give combinatorial (i.e., the mechanism does not invoke an LPsolver) polynomial time mechanisms for computing the leximin and leximax core imputations for the assignment game. These imputations achieve ``fairness'' in different ways: whereas leximin tries to make poor agents more rich, leximax tries to make rich agents less rich. In general, the two imputations are different. Our mechanisms were derived by a suitable adaptation of the classical primaldual paradigm from combinatorial optimization. The ``engine'' driving them involves recent insights, obtained via complementarity, into core imputations \cite{Va.Newcharacterizations} and the pristine combinatorial structure of matching. We have identified other natural games which could benefit from our approach. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.11437&r=gth 
By:  Kondiparthy, Venkata Tanay Kasyap (Warwick University) 
Abstract:  Mertens and Zamir (1985) first provided the universal type space construction for finite player games of incomplete information with a compact state space. Brandenburger and Dekel (1993) complemented it for a Polish state space. This paper extends the construction of Brandenburger and Dekel (1993) to games with infinitely many players for Harsanyiâ€™s notion of a type. The extension is formulated by randomly drawing a countably infinite set of actual players from a continuum of potential players, represented by their labels in [0, 1]. The random distribution of the countably infinite set of actual players almost surely converges to Lebesgue due to the Glivenkoâ€“Cantelli theorem. A coherent type is shown to induce beliefs over other playerâ€™s types and common knowledge of coherency closes the model of beliefs. Implications of dropping the Polish space assumption are discussed and an informal extension to measurable spaces is provided for future work. The formalisation provided here allows Harsanyiâ€™s notion of type to be applied in classes of games with many players such as Morris and Shin (2001) 
Keywords:  Higher Order Beliefs ; Universal Type Space ; Many Player Games JEL classifications: C70 ; D83 
Date:  2024 
URL:  http://d.repec.org/n?u=RePEc:wrk:wrkesp:72&r=gth 
By:  Zongxia Liang; Xiaodong Luo 
Abstract:  We study a reinsurance Stackelberg game in which both the insurer and the reinsurer adopt the meanvariance (abbr. MV) criterion in their decisionmaking and the reinsurance is irreversible. We apply a unified singular control framework where irreversible reinsurance contracts can be signed in both discrete and continuous times. The results theoretically illustrate that, rather than continuoustime contracts or a bunch of discretetime contracts, a single onceforall reinsurance contract is preferred. Moreover, the Stackelberg game turns out to be centering on the signing time of the single contract. The insurer signs the contract if the premium rate is lower than a timedependent threshold and the reinsurer designs a premium that triggers the signing of the contract at his preferred time. Further, we find that reinsurance preference, discount and reversion have a decreasing dominance in the reinsurer's decisionmaking, which is not seen for the insurer. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.11580&r=gth 
By:  Ville Korpela; Michele Lombardi; Riccardo Saulle 
Abstract:  We fully identify the class of social choice functions that are implementable in von Neumann Morgenstern (vNM) stable set (von Neumann and Morgenstern, 1944) by a rights structure. A rights structure formalizes the idea of power distribution in a society. Following Harsanyi’critique (Harsanyi, 1974), we also study implementation problems in vNM stable set that are robust to farsighted reasoning. 
Keywords:  Stable Set, Implementation, Rights Structure, Farsightedness 
JEL:  C71 D02 D71 D82 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:liv:livedp:202222&r=gth 
By:  Serena Wang; Michael I. Jordan; Katrina Ligett; R. Preston McAfee 
Abstract:  Rapid progress in scalable, commoditized tools for data collection and data processing has made it possible for firms and policymakers to employ ever more complex metrics as guides for decisionmaking. These developments have highlighted a prevailing challenge  deciding *which* metrics to compute. In particular, a firm's ability to compute a wider range of existing metrics does not address the problem of *unknown unknowns*, which reflects informational limitations on the part of the firm. To guide the choice of metrics in the face of this informational problem, we turn to the evaluated agents themselves, who may have more information than a principal about how to measure outcomes effectively. We model this interaction as a simple agency game, where we ask: *When does an agent have an incentive to reveal the observability of a costcorrelated variable to the principal?* There are two effects: better information reduces the agent's information rents but also makes some projects go forward that otherwise would fail. We show that the agent prefers to reveal information that exposes a strong enough differentiation between high and low costs. Expanding the agent's action space to include the ability to *garble* their information, we show that the agent often prefers to garble over full revelation. Still, giving the agent the ability to garble can lead to higher total welfare. Our model has analogies with price discrimination, and we leverage some of these synergies to analyze total welfare. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.14005&r=gth 
By:  Sylvain Béal (Université de FrancheComté, CRESE, UR3190, F25000 Besançon, France); Mostapha Diss (Université de FrancheComté, CRESE, UR3190, F25000 Besançon, France); Rodrigue Tido Takeng (Université de Caen, CREM, UMR6211, F14000 Caen, France) 
Abstract:  The Shapley and Owen values defined respectively for cooperative games with transferable utility (TUgames), and TUgames with coalition structure have recently been extended as allocation rules for TUgames with diversity constraints. This new class of games is introduced by B ́eal et al. (Working paper, 2024). In this new environment, players are divided into disjointed groups called communities. Diversity constraints require a mini mum number of members in each community for cooperation to take place. A coalition is diverse if it contains at least the required number of members from each community. The diversityrestricted game is a TUgame which assigns zero to any nondiverse coali tion and also assigns the original worth of a coalition if it is diverse. The extensions of the Shapley and Owen values are respectively called the Diversity Shapley value which is defined as the Shapley value of the diversityrestricted game, and the Diversity Owen value which is defined as the Owen value of the diversityrestricted game with coalition structure. Moreover, two axiomatic characterizations of these values are given. In this paper, we also present two new axiomatic characterizations of the Diversity Owen and Shapley values. 
Keywords:  TUgames, diversity constraints, axiomatic characterization, Diversity Shap ley value, Diversity Owen value. 
JEL:  C71 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:202409&r=gth 
By:  Seungjin Han; Alex Sam 
Abstract:  We study multidimensional signaling (cognitive/noncognitive) as a sender's portfolio choice with a resource constraint. We establish the existence of a unique monotone D1 equilibrium where the cognitive (noncognitive) signal increases (decreases) in sender type and the sum of the two increases in sender type. The equilibrium is characterized by two threshold sender types. The low threshold is one where a kink occurs in signaling. The constraint is binding only for sender types above it. The high threshold is the other one, above which all types spend all the resources in cognitive signal with pooling and discontinuity on the top. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.14003&r=gth 
By:  Siddhartha Bandyopadhyay (University of Birmingham); Moumita Deb (University of Heidelberg); Johannes Lohse (University of Birmingham); Rebecca McDonald (University of Birmingham) 
Abstract:  Majority voting is considered an efficient information aggregation mechanism in committee decisionmaking. We examine if this holds in environments where voters first need to acquire information from sources of varied quality and cost. In such environments, efficiency may depend on freeriding incentives and the 'transparency' regime  the knowledge voters have about other voters' acquired information. Intuitively, more transparent regimes should improve efficiency. Our theoretical model instead demonstrates that under some conditions, less transparent regimes can match the rate of efficient information aggregation in more transparent regimes if all members cast a vote based on the information they hold. However, a Pareto inferior swing voter's curse (SVC) equilibrium arises in less transparent regimes if less informed members abstain. We test this proposition in a lab experiment, randomly assigning participants to different transparency regimes. Results in less transparent regimes are consistent with the SVC equilibrium, leading to less favourable outcomes than in more transparent regimes. We thus offer the first experimental evidence on the effects of different transparency regimes on information acquisition, voting, and overall efficiency 
Keywords:  Information acquisition, Voting, Transparency, Swing voter's curse 
JEL:  C92 D71 D83 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:bir:birmec:2401&r=gth 
By:  SHINOZAKI, Hiroki 
Abstract:  We consider the object allocation problem with money. The seller owns multiple units of an object, and is only interested in her revenue from an allocation. Each buyer receives at most one unit of the object, and has a quasilinear utility function with private valuations. We study incentives of the seller to increase her revenue by introducing falsename buyers, i.e., shill bidding. An (allocation) rule is shillproof if the seller never benefits from introducing falsename buyers. A rule is a binary posted prices rule if there is a profile of posted prices such that whenever a buyer receives the object, she pays either her posted price or zero, and her payment is equal to zero when she does not receive the object. We show that if a rule satisfies shillproofness, strategyproofness, and nonimposition, then it is a binary posted prices rule. This result shows that the cost of preventing the seller from shill bidding is equivalent to the rigidity of the payment of each buyer, which highlights the difficulty in preventing the seller from shill bidding. It extends to a model of nonquasilinear utility functions with interdependent valuations. 
Keywords:  Shillproofness, Shill bidding, Strategyproofness, Posted prices rule, Binary posted prices rule, Multiunit auctions 
JEL:  D44 D47 D71 D82 
Date:  2024–02–13 
URL:  http://d.repec.org/n?u=RePEc:hit:hiasdp:hiase137&r=gth 
By:  Simona Fabrizi (Department of Economics and Centre for Mathematical Social Science, University of Auckland, New Zealand); Steffen Lippert (Department of Economics and Centre for Mathematical Social Science, University of Auckland, New Zealand.); Addison Pan (International Office and Centre for Mathematical Social Science, University of Auckland, New Zealand.); Matthew Ryan (School of Economics and Finance, Auckland University of Technology, New Zealand, and Centre for Mathematical Social Science, University of Auckland, New Zealand.) 
Abstract:  This paper considers a binary decision to be made by a committee canonically, a jury through a voting procedure. Each juror must vote on whether a defendant is guilty or not guilty. The voting rule aggregates the votes to determine whether the defendant is convicted or acquitted. We focus on the unanimity rule (convict if and only if all vote guilty), and we consider jurors who share ambiguous prior beliefs as in Ellis (2016). Our contribution is twofold. First, we identify all symmetric equilibria of these voting games. Second, we show that ambiguity may drastically undermine McLennan's (1998) results on decision quality: unlike in the absence of ambiguity, the ex ante optimal symmetric strategy profile need not be an equilibrium; indeed, there are games for which it is possible to reduce both types of error starting from any (nontrivial) equilibrium. 
Keywords:  : ambiguous priors, voting problems, decision quality 
JEL:  C02 D71 D81 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:aut:wpaper:202401&r=gth 
By:  Ville Korpela; Michele Lombardi; Riccardo Saulle 
Abstract:  otation programs are widely used in our society. For instance, a job rotation program is an HR strategy where employees rotate between two or more jobs in the same business. We study rotation programs within the standard implementation framework under complete information. When the designer would like to attain a Pareto efficient goal, we provide sufficient conditions for its implementation in a rotation program. However, when, for instance, every employee transitions through all different lateral jobs before rotating back to his original one, the conditions fully characterize the class of Pareto efficient goals that are implementable in rotation programs. 
Keywords:  Rotation Programs; Job Rotation; Assignment Problems; Implementation; Rights Structures; Stability 
JEL:  C71 D71 D82 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:liv:livedp:202221&r=gth 
By:  Villeneuve, Stéphane; Biais, Bruno; Gersbach, Hans; Rochet, JeanCharles; von Thadden, ErnstLudwig 
Abstract:  We analyze dynamic capital allocation and risk sharing between a principal and many agents, who privately observe their output. The state variables of the mechanism design problem are aggregate capital and the distribution of continuation utilities across agents. This gives rise to a Bellman equation in an infinite dimensional space, which we solve with meanfield techniques. We fully characterize the optimal mechanism and show that the level of risk agents must be exposed to for incentive reasons is decreasing in their initial outside utility. We extend classical welfare theorems by showing that any incentiveconstrained optimal allocation can be implemented as an equilibrium allocation, with appropriate money issuance and wealth taxation by the principal. 
Date:  2024–02–22 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:129131&r=gth 
By:  Yao Cheng; Zaifu Yang; Jingsheng Yu 
Abstract:  Multiple positions will be allocated to a group of individuals without side payments. Every individual has preferences over the positions, can have at most one position and may behave strategically. The right of using each position relies on individuals' given priorities. We propose a new solution called the proper exclusion right core which always guarantees to have precisely one solution. The solution is efficient, weakly and properly fair, can be supported by competitive prices and easily found by a procedure in a strategyproof way. It is built on a novel exclusion right system that respects priorities and maximizes selfconsistent exclusion rights. 
Keywords:  Core, proper exclusion right, indivisibility, incentive, top trading cycle. 
JEL:  C71 C78 D02 D47 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:yor:yorken:24/01&r=gth 
By:  Alessandro Marchesiani 
Abstract:  This paper studies how the structure of centralized markets may affect the efficient allocation in anonymous decentralized trades. In line with previous studies, we show that e¢ ciency in decentralized markets can be sustained in a moneyless Önitenumberofagents setting if agents are patient enough and the price is observed with noise as long as the noise disappears, but not too fast, as the number of agents grows. We also show that the LevinePesendorfer noise can be applied to dynamic games, not only to static games. 
Keywords:  Essentiality of money, anonymity, noisy prices, trading post 
Date:  2022–09 
URL:  http://d.repec.org/n?u=RePEc:liv:livedp:202223&r=gth 