Publications

Axiomatic Bargaining Theory: New Wine from Old Bottles (with Shiran Rachmilevitch, Games and Economic Behavior, forthcoming)

Five classical and uncontroversial axioms—symmetry, weak Pareto optimality, restricted monotonicity, midpoint domination, and superadditivity—characterize a bargaining solution. It assigns to each player their midpoint, that is, the n-th share of their utopia point, and equally divides what remains.

Belief Inducibility and Informativeness (with P. Jean-Jacques Herings and Toygar T. Kerman, Theory and Decision, 2024)

We consider a group of receivers who share a common prior on a finite state space and who observe private correlated messages that are contingent on the true state of the world. Our focus lies on the beliefs of receivers induced via the signal chosen by the sender and we provide a comprehensive analysis of the inducible distributions of posterior beliefs. Classifying signals as minimal, individually minimal, and language-independent, we show that any inducible distribution can be induced by a language-independent signal. We investigate the role of the different classes of signals for the amount of higher order information that is revealed to receivers. The least informative signals that induce a fixed distribution over posterior belief profiles lie in the relative interior of the set of all language-independent signals inducing that distribution.

Persuading and Sincere and Strategic Voters (with Toygar T. Kerman and P. Jean-Jacques Herings, Journal of Public Economic Theory, 2024)

A sender wants to persuade multiple homogeneous receivers to vote in favor of a proposal. Before the vote sender commits to a signal which sends private, potentially correlated, messages to receivers that are contingent on the true state of the world. The best equilibrium for sender in the resulting incomplete information game is unappealing: all receivers vote in favor of sender's preferred outcome, irrespective of their message. We therefore focus on the equilibrium where receivers vote sincerely, that is they vote in favor of the outcome that is optimal given their posterior. We characterize the optimal public and the optimal private signal, both for the case where receivers are behavioral and vote sincerely as well as the case where such behavior is a Bayes–Nash equilibrium (BNE). For the optimal public signal, sincere voting is a BNE, but the optimal private signal is subject to the swing voter's curse. Imposing the constraint that sincere voting be a BNE leads to an optimal signal where receivers are never pivotal.

Liability Situations with Successive Tortfeasors (with Frank Huettner, in: Advances in Collective Decision Making: Interdisciplinary Perspectives for the 21st Century (Eds: Sascha Kurz, Nicola Maaser, Alexander Mayer), 2023)

Given a tort that involves several tortfeasors, an allocation scheme attributes to each of them that part of the damage that reflects their responsibility. We consider successive torts—i.e., torts that involve a causality chain—and show that simple and intuitive principles, which are well-known in the law of tort, uniquely define an allocation scheme. We show that this scheme incentivizes agents to exhibit a certain level of care, creating an efficient prevention of accidents. We further describe the unique rule according to which a liability situation has to be adjusted after a partial settlement such that incentives to settle early are created.

Farsighted Rationalityin Hedonic Games (with G.-Herman Demeze-Jouatsa, Dynamic Games and Applications, 2023)

We consider a hedonic coalition formation game in which a coalition chooses for each partition of the player set the probability with which it forms and thereby destroys the current partition. These probabilities are commonly known so that farsighted players know at every partition what future partitions, and hence payoffs, will be reached with what probability. Thus, players can make rational decisions about the moves they support. We show that if coalitions make mistakes with small but positive probability, then there is a behavior profile in which no coalition has a profitable one-shot deviation.

Full Farsighted Rationality (with Laura Robles, Games and Economic Behavior, 2021)

An abstract game consists of a set of states, preferences over states, and an effectivity correspondence specifying what coalitions are allowed to replace one state by another one. Agents are called farsighted if, when deciding whether to support a coalition's move, they compare the status quo to the long term outcome following their deviation. Yet, this definition of farsightedness ignores a coalition's option to remain at the status quo allowing another coalition to move: agents are not fully farsighted. Therefore, we introduce extended expectation functions, which assign to each state a list of pairs consisting of a state and a coalition that is expected to move from the former to the latter. They endow agents with an expectation about what any deviation vis-a-vis maintaining the status quo entails. We impose three rationality axioms and provide a characterization of extended expectation functions that satisfy our axioms in terms of coalition behavior.

The Midpoint-constrained Egalitarian Bargaining Solution (with Shiran Rachmilevitch, Mathematical Social Sciences, 2019)

A payoff allocation in a bargaining problem is midpoint dominant if each player obtains at least one n-th of her ideal payoff. The egalitarian solution of a bargaining problem may select a payoff configuration which is not midpoint dominant. We propose and characterize the solution which selects for each bargaining problem the feasible allocation that is closest to the egalitarian allocation, subject to being midpoint dominant. Our main axiom, midpoint monotonicity, is new to the literature; it imposes the standard monotonicity requirement whenever doing so does not result in selecting an allocation which is not midpoint dominant. In order to prove our main result we develop a general extension theorem for bargaining solutions that are order-preserving with respect to any order on the set of bargaining problems.

A Generalisation of the Egalitarian and the Kalai-Smorodinsky Bargaining Solutions (with Nozomu Muto and Shiran Rachmilevitch, The International Journal of Game Theory, 2018)

We characterize the class of weakly efficient n-person bargaining solutions that solely depend on the ratios of the players’ ideal payoffs. In the case of at least three players the ratio between the solution payoffs of any two players is a power of the ratio between their ideal payoffs. As special cases this class contains the Egalitarian and the Kalai–Smorodinsky bargaining solutions, which can be pinned down by imposing additional axioms.

Effectivity and Power (with Hans Peters, Games and Economic Behavior, 2018)

We axiomatically develop a class of power indices for effectivity functions, both for the case where the set of alternatives is finite and where it is infinite. Such power indices make it possible to take the issues under consideration into account, in contrast to power indices defined just for simple games. As an example, we consider the US legislative system. We also show that our approach can be used to develop power indices for spatial political games.

A note on monotonic power indices, smaller coalitions, and new members (Theory and Decision, 2016)

Brams’ paradox of new members and Shenoy’s paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley–Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.

Stable partitions for games with non-transferable utilities and externalities (The International Journal of Game Theory, 2015), Working Paper

I propose a model of coalitional bargaining with claims in order to find solutions for games with non-transferable utility and externalities. I show that, for each such game, payoff configurations exist which will not be renegotiated. In the ordinal game derived from these payoff configurations, a core stable partition can be found, i.e. a partition in which no group of players has an incentive to jointly change their coalitions.

Indirect control and power in mutual control structures (with Hans Peters, Games and Economic Behavior, 2015)

In a mutual control structure (mcs) agents exercise control over each other. Typical examples occur in the area of corporate governance: firms and investment companies exercise mutual control, in particular by owning each others' stocks. We represent such situations in two equivalent ways: by a function assigning to each coalition the set of controlled players, and by a simple game structure in which for each player a simple game describes who controls that player. These concepts are similar to authority distributions and command games in Hu and Shapley, 2003a, Hu and Shapley, 2003b. An mcs is invariant if it incorporates all indirect control relations. We axiomatically develop a class of power indices for invariant mcs. We impose four axioms with a plausible interpretation in this framework, which together characterize a broad class of power indices based on dividends resulting both from exercising and from undergoing control. Extra conditions can further refine this broad class.

Coalition formation in general apex games under monotonic power indices (Games and Economic Behavior, 2014)

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.