
on Game Theory 
By:  Emanuel Tewolde 
Abstract:  In the literature on simultaneous noncooperative games, it is wellknown that a positive affine (linear) transformation (PAT) of the utility payoffs do not change the best response sets and the Nash equilibrium set. PATs have been successfully used to expand the classes of 2player games for which we can compute a Nash equilibrium in polynomial time. We investigate which game transformations other than PATs also possess one of the following properties: (i) The game transformation shall not change the Nash equilibrium set when being applied on an arbitrary game. (ii) The game transformation shall not change the best response sets when being applied on an arbitrary game. First, we prove that property (i) implies property (ii). Over a series of further results, we derive that game transformations with property (ii) must be positive affine. Therefore, we obtained two new and equivalent characterisations with game theoretic meaning for what it means to be a positive affine transformation. All our results in particular hold for the 2player case of bimatrix games. 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.00076&r= 
By:  Gisèle Umbhauer 
Abstract:  Arad and Rubinstein’s 1120 money request game nicely triggers levelk reasoning. Yet we show that mixedstrategy minimax regret, in a general class of moneyrequest games, mimics a levelk reasoning, at least if the number of players is supposed to decrease in the depth of reasoning. We also show that, in this class of games, the minimax regret probability distribution is the exact reverse of the mixedstrategy Nash equilibrium distribution, and that minimax regret leads to a larger expected payoff than the Nash equilibrium payoff. 
Keywords:  minimax regret, levelk reasoning, moneyrequest game, Nash equilibrium. 
JEL:  C72 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ulp:sbbeta:202148&r= 
By:  Lucas Pahl 
Abstract:  This paper considers an infinitely repeated threeplayer Bayesian game with lack of information on two sides, in which an informed player plays two zerosum games simultaneously at each stage against two uninformed players. This is a generalization of the Aumann et al. [1] twoplayer zerosum onesided incomplete information model. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his longterm average payoffs. Our objective is to understand the adverse effects of \information spillover" from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects and characterize equilibrium payoffs. In a second result, we show how the effects of information spillover on the equilibrium payoff set of the informed player might be severe. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.01647&r= 
By:  Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Marialaura Pesce (Università di Napoli Federico II and CSEF); Maria Romaniello (Università degli Studi della Campania Luigi Vanvitelli.) 
Abstract:  We consider pure exchange economies with finitely many private goods including also nonSamuelsonian public goods. For this type of economies, the notion of competitive equilibrium called cost share equilibrium is founded on individual payments for public goods varying according to individual benefits. This situation naturally arises when a level of provision is interpreted as a whole configuration of public policies or when cost share functions are interpreted as voluntary contributions instead of predetermined tax systems (Mas Colell (1980)). We establish the equivalence of cost share equilibria with cooperative and noncooperative gametheoretic solutions. In particular: 1. we characterize cost share equilibria as those allocations which cannot be improved upon by the society; 2. we characterize cost share equilibria as Nash equilibria of a game with two players. Then we discuss the existence of cost share equilibria in economies with public projects satisfying standard assumptions and provide a condition for the set of cost share equilibria to be nonempty. Our analysis of cooperative solutions is based on contribution schemes which capture the fraction of the total cost of collective goods that each coalition of agents is expected to cover. 
Keywords:  NonSamuelsonian public goods, Cost share equilibrium, Aubin core, Nash equilibrium. 
JEL:  D49 D51 C72 
Date:  2021–11–12 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:628&r= 
By:  Thomas Giebe; Radosveta IvanovaStenzel; Martin G. Kocher; Simeon Schudy 
Abstract:  Overbidding in secondprice auctions (SPAs) has been shown to be persistent and associated with cognitive ability. We study experimentally to what extent crossgame learning can reduce overbidding in SPAs, taking into account cognitive skills. Employing an orderbalanced design, we use firstprice auctions (FPAs) to expose participants to an auction format in which losses from high bids are more salient than in SPAs. Experience in FPAs causes substantial crossgame learning for cognitively less able participants but does not affect overbidding for the cognitively more able. Vice versa, experiencing SPAs before bidding in an FPA does not affect bidding behavior by the cognitively less able but, somewhat surprisingly, reduces bid shading by cognitively more able participants, resulting in lower profits in FPAs. Thus, crossgame learning has the potential to benefit bidders with lower cognitive ability whereas it has little or even adverse effects for higher ability bidders. 
Keywords:  cognitive ability, crossgame learning, experiment, auction, heuristics, firstprice auctions, secondprice auctions 
JEL:  C72 C91 D44 D83 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9396&r= 
By:  Ilwoo Hwang; Jee Seon Jeon 
Abstract:  We study an infinitehorizon multilateral bargaining game in which the status quo policy, players¡¯ recognition probabilities, and their voting weights are endogenously determined by the previous bargaining outcome. With players not discounting future payoffs, we show that the longrun equilibrium outcome features the concentration of power by one or two players, depending on the initial bargaining state. If the players¡¯ initial shares are relatively equal, they successfully prevent tyranny, but a twoplayer oligarchy nevertheless emerges and persists. The same results are obtained with payoff discounting, provided that the players¡¯ shares are not too small. Our results highlight the importance of the initial power distribution and discounting of future payoffs in the longrun development of power configuration. 
Keywords:  Dynamic bargaining; Endogenous political power; Endogenous institution; Markov perfect equilibrium, Oligarchy; 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:snu:ioerwp:no145&r= 
By:  Endre Cs\'oka 
Abstract:  Athey and Segal introduced an efficient budgetbalanced mechanism for a dynamic stochastic model with quasilinear payoffs and private values, using the solution concept of perfect Bayesian equilibrium (PBE). However, this implementation is not robust in multiple senses. For example, we will show a generic setup where the efficient strategy profiles can be eliminated by iterative elimination of weakly dominated strategies. Furthermore, this model used strong assumptions about the information of the agents, and the mechanism was not robust to the relaxation of these assumptions. In this paper, we will show a different mechanism that implements efficiency under weaker assumptions and using the stronger solution concept of "efficient Nash equilibrium with guaranteed expected payoffs". 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2110.15219&r= 
By:  John Duffy; Lucie Lebeau; Daniela Puzzello 
Abstract:  We report on an experiment in which buyers and sellers engage in semistructured bargaining in two dimensions: how much of a good the seller will produce and how much money the buyer will offer the seller in exchange. Our aim is to evaluate the empirical relevance of two axiomatic bargaining solutions, the generalized Nash bargaining solution and Kalai's proportional bargaining solution. These bargaining solutions predict different outcomes when buyers are constrained in their money holdings. We first use the case when the buyer is not liquidity constrained to estimate the bargaining power parameter, which we find to be equal to 1/2. Then, imposing liquidity constraints on buyers, we find strong evidence in support of the Kalai proportional solution and against the generalized Nash solution. Our findings have policy implications, e.g., for the welfare cost of inflation in searchtheoretic models of money. 
Keywords:  Bargaining; Monetary Economics; Experimental Economics 
JEL:  C78 C92 D83 
Date:  2021–11–10 
URL:  http://d.repec.org/n?u=RePEc:fip:feddwp:93380&r= 
By:  Barelli, Paulo (?); Govindan, Srihari (?); Wilson, Robert (Stanford U) 
Abstract:  We posit a standard model of an asymmetric double auction with interdependent values in which each trader observes a private signal about a hidden state before submitting a bid or ask price for a unit demand or supply. The state and signals are onedimensional, tradersâ€™ signals are independent conditional on the state, and their distributions have the strict monotone likelihood ratio property. The model encompasses auctions by allowing sellers to be nonstrategic. We study a version in which there are n replicates of each type of trader, with each replicate observing a signal drawn independently from the same conditional distribution as the original trader of that type, and all traders of the same type using the same strategy. The limit economy with a countable set of traders has a unique Walrasian equilibrium, whose clearing price reveals the state. If this equilibrium is totally monotone in that each buyer's (resp. seller's) probability of trading decreases (resp. increases) with the state, then the limit auction has a monotone equilibrium yielding the Walrasian price as the clearing price. We present four asymptotic results as n grows large: (1) a sequence of monotone strategies comprises epsilonequilibria iff limit points are monotone equilibria of the limit auction; (2) for a sequence of monotone strategy profiles converging to a monotone equilibrium, the Strong Law of Large Numbers for prices holds, in that the sequence of price functions converges a.s. to the price function of the limit equilibrium; (3) if the effect of the state on traders' valuations is symmetric (around the equilibrium) then large but finite auctions have monotone equilibria whose outcomes approximate the Walrasian equilibrium outcome when bidders are restricted to sufficiently fine bidgrids; and (4) the same conclusion holds true without the symmetry assumption when we discretize the state space as well. Total monotonicity seems to be crucial: an example has a Walrasian equilibrium that is not the outcome of a Nash equilibrium of an auction. 
JEL:  C7 D44 D82 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:3984&r= 
By:  Tim Ritmeester; Hildegard MeyerOrtmanns 
Abstract:  We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the reaction of the market to individual actions of the agents as well as the reaction of the agents to individual information items of the market, from which we derive a selfconsistent solution to the minority game. In particular we analyze the impact of general nonlinear price functions on the amount of arbitrage if noise from external fluctuations is present. We identify the conditions under which arbitrage gets reduced due to the presence of noise. When the cavity method is extended to time dependent response of the market price to previous actions of the agents, the individual contributions of noise from external fluctuations in price and information and from noise due to the choice of strategies can be pursued in the transient dynamics until a stationary state is reached. It explains the time evolution of scores of the agents' strategies: it changes from initially a random walk to bounded excursions on an intermediate time scale to effectively random switching in the choice between strategies. In contrast to a CurieWeiss level of a meanfield approach, the market response included by the cavity method captures the realistic feature that the agents have a preference for a certain choice of strategies without getting stuck to a single choice. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.06663&r= 
By:  Claude Fluet; Thomas Lanzi 
Abstract:  Two opposed parties seek to ináuence an uninformed decision maker. They invest in acquiring information and select what to disclose. The decision maker then adjudicates. We compare this benchmark with a procedure allowing adversarial crossexamination. A crossexaminer tests the opponent in order to persuade the decision maker that the opponent is deceitful. How does the opportunity or threat of crossexamination affect the parties' behavior? How does it affect the quality of decisionmaking? We show that decisionmaking deteriorates because parties are less likely to acquire information and because crossexamination too often makes the truth appear as falsehood. Next, we consider a form of controlled crossexamination by permitting the crossexamined to be reexamined by his own advocate, i.e., counterpersuasion. More information then reaches the decision maker. Decisionmaking may or may not improve compared to the benchmark depending on how examination is able to trade off type 1 and 2 errors. 
Keywords:  Bayesian persuasion, disclosure game, adversarial, redirect examination, procedural rules. 
JEL:  C72 D71 D82 D83 K41 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ulp:sbbeta:202140&r= 
By:  Seungjin Han; Siyang Xiong 
Abstract:  This paper provides a unified approach to equilibrium analysis in models for competing mechanisms (e.g., Szentes (2009), Yamashita (2010)), which may differ in terms of delegation of action choice, announcement of mechanisms, observability of messages, and equilibrium notions. 
Keywords:  competing mechanisms; unified equilibrium analysis; multiple principals 
JEL:  D82 C79 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:mcm:deptwp:202109&r= 
By:  Ennio Bilancini (IMT School for Advanced Studies, Lucca (I)); Leonardo Boncinelli (University of Florence); Alessandro Tampieri (University of Florence) 
Abstract:  This paper investigates the role of strategy assortativity for the evolution of parochial ism. Individuals belonging to different groups are matched in pairs to play a prisoner dilemma, conditioning their choice on the identity of the partner. Strategy assortativ ity implies that a player is more likely to be matched with someone playing the same strategy. We find that, if the degree of strategy assortativity is sufficiently high, then parochialism (i.e., cooperate with your own group and defect with others) spreads over a group, while egoism (i.e., defect with everyone) emerges otherwise. Notably, parochialism is more likely to emerge in a smaller group. 
Keywords:  prisoner dilemma; cooperation; ingroup favoritism; cultures; asymptotic stability. 
JEL:  C72 C73 Z10 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:luc:wpaper:2120&r= 
By:  Konrad Menzel 
Abstract:  We provide asymptotic approximations to the distribution of statistics that are obtained from network data for limiting sequences that let the number of nodes (agents) in the network grow large. Network formation is permitted to be strategic in that agents' incentives for link formation may depend on the ego and alter's positions in that endogenous network. Our framework does not limit the strength of these interaction effects, but assumes that the network is sparse. We show that the model can be approximated by a sampling experiment in which subnetworks are generated independently from a common equilibrium distribution, and any dependence across subnetworks is captured by state variables at the level of the entire network. Under manyplayer asymptotics, the leading term of the approximation error to the limiting model established in Menzel (2015b) is shown to be Gaussian, with an asymptotic bias and variance that can be estimated consistently from a single network. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.01678&r= 
By:  Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) 
Abstract:  We introduce a generalization of the MaschlerPerles bargaining solution to smooth bargaining problems for $n$ players. We proceed by the construction of measures on the Pareto surface of a convex body. The MP surface measure is defined for Cephoids, i.e., Minkowski sums of simplices (see [14] for a coherent description); this measure cannot directly be extended to a smooth Pareto surface. Therefore, we introduce a further extension of the MaschlerPerles idea to Pareto surfaces of convex bodies. This extension is suggested by the density $\sqrt[n]{n_1\cdots n_n }$ of normals in coordinate directions  a term generalizing the MaschlerPerles line integral of $\sqrt{dx_1 dx_2}$  the "donkey cart" in their interpretation. The "deGua'' measure defined this way, is then verified to be the limiting measure of the MP measures along the filter of convergent Cephoids as established in [15]. 
Date:  2021–11–22 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:658&r= 
By:  Rastislav Rehak; Maxim Senkov 
Abstract:  We study a Bayesian persuasion model in which the state space is finite, the sender and the receiver have statedependent quadratic loss functions, and their disagreement regarding the preferred action is of arbitrary form. This framework enables us to focus on the understudied sender’s tradeoff between the informativeness of the signal and the concealment of the statedependent disagreement about the preferred action. In particular, we study which states are pooled together in the supports of posteriors of the optimal signal. We provide an illustrative graph procedure that takes the form of preference misalignment and outputs potential representations of the statepooling structure. Our model provides insights into situations in which the sender and the receiver care about two different but connected issues, for example, the interaction of a political advisor who cares about the state of the economy with a politician who cares about the political situation. 
Keywords:  Bayesian persuasion; strategic state pooling; preference misalignment; graph procedure; 
Date:  2021–10 
URL:  http://d.repec.org/n?u=RePEc:cer:papers:wp708&r= 
By:  Han Jiang (Department of Economics, University of Ottawa); Aggey Simons (Department of Economics, University of Ottawa) 
Abstract:  This paper presents a dynamic model of charitable giving. At each period, donors contribute to a nonprofit organizationâ€™s (NPO) endowment; the NPO provides a charitable good and invests in the financial market. Investments are made in a risky asset and a riskfree asset. To account for uncertainty, we introduce two types of shocks: donorsâ€™ income shock and financial market fluctuations. We show that the optimal share of disposable endowment, invested in risky asset, is constant. Donorsâ€™ strategy, whether to contribute or freeride on the NPOâ€™s investments, depends on donorsâ€™ shadow prices. Donors contribute when NPOâ€™s endowment is relatively low. Large contribution levels encourage the NPO to participate in the capital market at the expense of providing charitable good. We show that the NPO prefers an environment with a lower rate of return on riskfree asset. NPOâ€™s risk exposure to the financial market affects both NPOâ€™s and donorsâ€™ decisions. However, risk exposures on donorsâ€™ side do not have any impact on partiesâ€™ decisions. Regulation analysis suggests that portfolio ceiling and provision floor are achievable. 
Keywords:  Voluntary Contribution, Public Goods, Charitable Investment, Risk Preference, Stochastic Differential Game, GaussMarkov Process, HamiltonJacobiBellman Equations. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ott:wpaper:2113e&r= 
By:  Ivonne Callejas; Srihari Govindan; Lucas Pahl 
Abstract:  Govindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.01638&r= 
By:  Johari, Ramesh (Stanford U); Light, Bar (Stanford U); Weintraub, Gabriel Y. (Stanford U) 
Abstract:  Online platforms collect rich information about participants and then share some of this information back with them to improve market outcomes. In this paper we study the following information disclosure problem in twosided markets: If a platform wants to maximize revenue, which sellers should the platform allow to participate, and how much of its available information about participating sellers' quality should the platform share with buyers? We study this information disclosure problem in the context of two distinct twosided market models: one in which the platform chooses prices and the sellers choose quantities (similar to ridesharing), and one in which the sellers choose prices (similar to ecommerce). Our main results provide conditions under which simple information structures commonly observed in practice, such as banning certain sellers from the platform while not distinguishing between participating sellers, maximize the platform's revenue. An important innovation in our analysis is to transform the platform's information disclosure problem into a constrained price discrimination problem. We leverage this transformation to obtain our structural results. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:3905&r= 