We characterize three interrelated solution concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model in a framework with incomplete information. Based on it, we give two groups of conditions; one characterizes permissibility and proper rationalizability, the other characterizes permissibility in an alternative

We study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing

In this paper we offer a new, unifying approach to modeling strategies of bounded complexity. In our model, the strategy of a player in a game does not directly map the set H of histories to the set of her actions. Instead, the player’s perception of H is represented by a map \(\varphi :H \rightarrow X,\) where X reflects the “cognitive complexity” of the player, and the strategy chooses its mixed

The purpose of this paper is to study which coalition structures have stable distributions. We employ the projective core as a stability concept. Although the projective core is often defined only for the grand coalition, we define it for every coalition structure. We apply the core notion to a variety of economic models including the public goods game, the Cournot and Bertrand competition, and the

We justify risk neutral equilibrium bidding in commonly known fair division games with incomplete information by an evolutionary setup postulating (i) minimal common knowledge, (ii) optimal responses to conjectural beliefs how others behave and (iii) evolutionary selection of conjectural beliefs with fitness measured by expected payoffs. After justifying the game forms we derive the evolutionary games

We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are

This paper analyzes the set of pure strategy subgame perfect Nash equilibria of any finitely repeated game with complete information and perfect monitoring. The main result is a complete characterization of the limit set, as the time horizon increases, of the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely repeated game. This model includes the special case of observable

An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum

We give sufficient and necessary conditions for the non-emptiness of the alpha-core in the setting of strategic games with non-ordered and discontinuous preferences. In order to prove our results, we can avoid the use of Scarf’s Theorem for NTU-games, by suitably appealing to the Ky Fan minimax inequality. Examples clarify our conditions and allow the comparison of our results with the previous ones

This note shows that the work by Simon and Tomkowicz (Israel J Math 227(1):215–231, 2018) answers another outstanding open question in game theory in addition to the non-existence of approximate Harsányi equilibrium in Bayesian games: it shows that strategic form games with bounded and separately continuous payoffs need not possess approximate equilibria.

We study first-price auctions in which the number of bidders is the seller’s private information, and investigate the use of a reserve price to signal this private information. We use the D1 criterion to refine the set of equilibria and characterize a symmetric separating equilibrium outcome, where the reserve price increases with the number of bidders. The key driving force is a certain form of single-crossing

We consider auctions where bidders’ valuations are positively correlated with their productivity in a second-stage aftermarket. We test in the lab whether bidders recognize the opportunity to signal their productivity through their bidding and, conditional on them doing so, whether disclosing different information about the auction outcomes affects their signaling behavior. Our results confirm that

We follow the Nash program to provide a new strategic justification of the Talmud rule in bankruptcy problems. The design of our game is based on a focal axiomatization of the rule, which combines consistency with meaningful lower and upper bounds to all creditors. Our game actually considers bilateral negotiations, inspired by those bounds, which are extended to an arbitrary number of creditors, by

We provide an exact analytical solution of the Nash equilibrium for the kth price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

We study Tullock contests with n symmetric players. We show that in a contest without an exit option, if prizes and punishments (negative prizes) have the same cost, it is optimal for the designer who wants to maximize the players’ total effort to allocate the entire prize sum to a single punishment without any prize. On the other hand, in a contest with an exit option, it is optimal to allocate the

We prove some interesting properties of unilaterally competitive games when there are more than two players. We show that such games possess: (1) a Nash equilibrium, (2) maximin-solvability, (3) strong solvability in the sense of Nash, and (4) weak acyclicity, all in pure strategies of finite or infinite games.

We study strong Nash equilibria in mixed strategies in finite games. A Nash equilibrium is strong if no coalition of players can jointly deviate so that all players in the coalition get strictly better payoffs. Our main result concerns games with two players and states that if a game admits a strong Nash equilibrium, then the payoff pairs in the support of the equilibrium lie on a straight line in

Joint debts are debts that more than one debtor guarantees mutually. They are sometimes interpreted as a version of the tragedy of the commons. However, a simple model of the dynamic tragedy of the commons fails to capture an important feature of joint debts. The authors model joint debts as a joint borrowing limit game and compare the model with the dynamic tragedy of the commons model. Thereby, the

This paper proposes a dynamic model for the process of industry consolidation by sequences of mergers and acquisitions that create synergy gains to merging firms and may impose positive or negative externalities on the remaining firms in the industry. We allow firms to make acquisition offers that are conditional and unconditional on acceptances of target firms, instead of the usual conditional offers

This paper is concerned with an old question: Will oligopolistic firms have incentives to merge to monopoly and will the monopoly, if the firms indeed merge, be stable? To answer this question, I motivate and introduce a new core concept for a general partition function game and prove stability of the merger-to-monopoly by applying the new core concept, labelled the strong-core, to Cournot oligopoly

We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot–Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (Econometrica 41:467–501, 1973), that

In a class of asymmetric-cost duopoly price competition games, price-elastic individual demand reveals a threshold of informed buyers below which equilibrium is in monopoly prices. Even if the threshold is met, unless all buyers are informed, monopoly prices are listed and are more likely between less alike sellers. An increase in the efficient seller’s cost weakly reduces its rival’s price (in a first

We use a first-capacity-then-price-setting game as a theoretical benchmark for an experimental study which identifies capacity precommitment, intra-play communication, and prior experience as crucial factors for collusive pricing. The theoretical model determines capacity thresholds above which firms have an incentive to coordinate on higher than equilibrium prices. The experimental data confirm that

Given a set of combinatorial games, the children are all those games that can be generated using as options the games of the original set. It is known that the partial order of the children of all games whose birthday is less than a fixed ordinal is a distributive lattice and also that the children of any set of games form a complete lattice. We are interested in the converse. In a previous paper,

We introduce the idea that a player believes at every stage of a dynamic game that his opponents will choose rationally in the future and have chosen rationally in a restricted way in the past. This is summarized by the concept of common belief in future and restricted past rationality, which is defined epistemically. Moreover, it is shown that every properly rationalizable strategy of the normal form

We examine how democratic mechanisms can yield socially desirable outcomes in the presence of uncertainty about an underlying state of nature. We depart from a conventional mechanism design approach because we aim for democratic mechanisms to reflect some basic properties of decision-making in democracies. In particular, actual decisions are made by majority voting. The proposals to be voted upon are

This paper axiomatically studies the equal split-off set (cf. Branzei et al. (Banach Center Publ 71:39–46, 2006)) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (Econometrica 57:615–635, 1989) solution for convex games. By deriving several characterizations, we explore consistency of the equal split-off set on the domains of exact partition

What networks can form and persist when agents are self-interested? Can such networks be efficient? A substantial theoretical literature predicts that various networks emerge randomly and efficiency is unlikely to be sustained, but these predictions are in stark contrast to empirical findings. In this paper, we present a new model of network formation. In contrast to the existing literature, we assume

We consider a collective choice problem in which the number of alternatives and the number of voters vary. Two fundamental axioms of consistency in such a setting, reinforcement and composition-consistency, are incompatible. We first observe that the latter implies four conditions each of which can be formulated as a consistency axiom on its own right. We find that two of these conditions are compatible

The opinions of a group of experts must be aggregated to determine the deserving winner of a competition. The procedure of aggregation is majoritarian if, whenever a majority of experts honestly believe that a contestant is the best, the given contestant is considered the deserving winner. The fact that an expert believes that a contestant is the best does not necessarily imply that he/she wants this

A game is solvable if the set of Nash equilibria is nonempty and interchangeable. A pairwise solvable game is a two-person symmetric game in which any restricted game generated by a pair of strategies is solvable. We show that the set of equilibria in a pairwise solvable game is interchangeable. Under a quasiconcavity condition, we derive a complete order-theoretic characterization and some topological

I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across

The Rock–scissors–paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter

We develop a model of two parallel contests, asymmetric in quantity of homogeneous prizes open to contest, with a finite number of homogeneous risk-neutral bidders. Whether the bidder upon entry into a particular contest is aware of the realized number of competing contestants in the contest is irrelevant to the expected effort at equilibrium. At equilibrium the expected effort per capita in the larger

This paper extends the concept of face games, introduced by González-Díaz and Sánchez-Rodríguez (Games Econ Behav 62:100–105, 2008) for convex games, to the general class of balanced games. Each face of the core is the core of a face game and contains the best stable allocations for a coalition provided that the members of the complement coalition get their miminum worth inside the core. Since face

A new concept for TU-values, called value dividends, is introduced. Similar to Harsanyi dividends, value dividends are defined recursively and provide new characterizations of values from the Harsanyi set. In addition, we generalize the Harsanyi set where each of the TU-values from this set is defined by the distribution of the Harsanyi dividends via sharing function systems and give an axiomatic characterization

I study the following repeated version of Nash’s Demand Game: whenever the demands are not jointly compatible, the player who stated the lower demand (the less greedy player) obtains the following advantage: his offer is the only one “on the table”, and the greedier player needs to respond to this offer by either accepting it (which terminates the game) or rejecting it (which triggers a one-period

This paper studies a principal-agent relationship when both are risk-neutral and in the presence of adverse selection and moral hazard. Contracts must satisfy the limited-liability and monotonicity conditions. We provide sufficient conditions under which the optimal contract is simple, in the sense that each type is offered the same contract. These are: the action and the agent’s type are complements

We study the bilateral trading problem under private information. We characterize the range of possible mechanisms which satisfy ex-post efficiency, incentive compatibility, individual rationality, and budget balance. In particular, we show that the famous Myerson–Satterthwaite impossibility result no longer holds when contingent contracts are allowed.

We analyze a bargaining model which is a generalization of the model of Rubinstein (Econometrica 50(1):97–109, 1982) from the viewpoint of the process of how a proposer is decided in each period. In our model, a player’s probability to be a proposer depends on the history of proposers and players divide a pie of size 1. We derive a subgame perfect equilibrium (SPE) and analyze how its SPE payoffs are

In this paper, we evaluate in the context of weighted (j, k)-simple games, the maximal degree of perturbations which may be allowed, in voters weights and/or in the quotas, without changing the structure of the game. For this purpose, we extend on (j, k)-simple games the notion of amplitude well known for ordinary simple games. Recall that, (j, k)-simple games provide a model of decision making in

We develop a novel model of price-fee competition in bilateral oligopoly markets with non-expandable infrastructures and costly transportation. The model captures a variety of real market situations and it is the continuous quantity version of the assignment game with indivisible goods on a fixed network. We define and characterize stable market outcomes. Buyers exclusively trade with the supplier

We introduce set packing games as an abstraction of situations in which n selfish players select disjoint subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this basic class of games. Special attention is given to a subclass of set packing games, namely throughput scheduling games, where the items represent jobs, and the subsets that a player can select

We introduce a new axiom for power indices, which requires the total (additively aggregated) power of the voters to be nondecreasing in response to an expansion of the set of winning coalitions; the total power is thereby reflecting an increase in the collective power that such an expansion creates. It is shown that total-power monotonic indices that satisfy the standard semivalue axioms are probabilistic

In two-sided markets with transferable utility (‘assignment games’), we study the dynamics of trade arrangements and price adjustments as agents from the two market sides stochastically match, break up, and re-match in their pursuit of better opportunities. The underlying model of individual adjustments is based on the behavioral theories of adaptive learning and aspiration adjustment. Dynamics induced

Core-selecting auctions were proposed as alternatives to the Vickrey–Clarke–Groves (VCG) mechanism for environments with complementarities. In this paper, we consider a simple incomplete-information model that allows correlations among bidders’ values. We perform a full equilibrium analysis of three core-selecting auction formats as applied to the “local-local-global” model. We show that seller revenues

This study investigates how externalities from downstream competition shape sorting in upstream labor markets. I model this as a two-stage game: A first stage of simultaneous one-to-one matching between firms and managers and a second stage of Cournot competition among matched pairs. If a firm’s technology and human capital are strategic complements, it is rational for each firm-manager pair to expect

We present results from a series of experiments that allow us to measure overbidding and, in particular, underbidding in first-price auctions. We investigate the extent to which the amount of underbidding depends on the seemingly innocuous parameters of the experimental setup. To structure our data, we present and test a theory that introduces constant markdown bidders into a population of fully rational

This article presents an axiomatic characterization of a new value for cooperative games with incomplete communication. The result is obtained by slight modifications of associated games proposed by Hamiache (Games Econ Behav 26:59–78, 1999; Int J Game Theory 30:279–289, 2001). This new associated game can be expressed as a matrix formula. We generate a series of successive associated games and show

We consider linearly weighted versions of the least core and the (pre)nuceolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by

This paper studies an idea we call “(null) self-recognition,” which occurs when a player who was certain that they were a particular type privately discovers that they are in fact some other type. To address unresolved questions as to how players update their beliefs regarding their partner’s type and higher-order beliefs regarding both players’ types after self-recognition, we propose a “sequential

In this paper, we introduce a solution concept generalizing the Harsanyi non-transferable utility (NTU) value to cooperative games with incomplete information. The so-defined S-solution is characterized by virtual utility scales that extend the Harsanyi-Shapley fictitious weighted-utility transfer procedure. We construct a three-player cooperative game in which Myerson’s (Int J Game Theory 13(2):69–96

This paper studies a job market signaling model with imperfect competition among employers. In our basic model, workers are differentiated in productivity and preference over employers, both of which are workers’ private information. We conclude that if competition is sufficiently strong, a separating equilibrium exists. We also show that stronger competition among employers intensifies competition

We consider land rental problems where there are several communities that can act as lessors and a single tenant who does not necessary need all the available land. A rule should determine which communities become lessors, how much land they rent and at which price. We present a complete characterization of the family of rules that satisfy reassignment-proofness by merging and spliting, apart from

The problem of fair division of payoff is one of the key issues when considering cooperation of strategic individuals. It arises naturally in a number of applications related to operational research, including sharing the cost of transportation or dividing the profit among supply chain agents. In this paper, we consider the problem of extending the Shapley Value—a fundamental payoff division scheme—to

I study a strategic-communication game between an informed sender and an uninformed receiver with partially aligned preferences. The receiver is endowed with the ability to probabilistically detect if the sender is lying. Specifically, if the sender is making a false claim about her type, with some commonly known probability p the receiver additionally observes a private signal indicating that the

Riordan and Sappington (J Econ Theory 45:189–199, 1988) show that in an agency relationship in which the agent’s type is correlated with a public ex post signal, the principal may attain first best (full surplus extraction and efficient output levels) if the agent is faced with a lottery such that each type is rewarded for one signal realization and punished equally for all the others. Gary-Bobo and

We provide comparable algorithms for the Dekel–Fudenberg procedure, iterated admissibility, proper rationalizability and full permissibility by means of the notions of likelihood orderings and preference restrictions. The algorithms model reasoning processes whereby each player’s preferences over his own strategies are completed by eliminating likelihood orderings. We apply the algorithms for comparing

A tournament can be represented as a set of candidates and the results from pairwise comparisons of the candidates. In our setting, candidates may form coalitions. The candidates can choose to fix who wins the pairwise comparisons within their coalition. A coalition is winning if it can guarantee that a candidate from this coalition will win each pairwise comparison. This approach divides all coalitions

Using a network approach we provide a characterization of a separating equilibrium for standard signaling games where the sender’s payoff function is quasi-linear. Given a strategy of the sender, we construct a network where the node set and the length between two nodes are the set of the sender’s type and the difference of signaling costs, respectively. Construction of a separating equilibrium is