Oriol Tejada

Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

We extend the notion of symmetrically pairwise-bargained (SPB) allocations (Rochford, J Econ Theory, 34:262–281, 1984) to balanced assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent’s payoff remains invariant after a negotiation process between all agents based on what they could receive—and use as a threat—in their preferred alternative matching to any given optimal matching. We prove that, for balanced multi-sided assignment games, the set of SMB is always nonempty and that, unlike the two-sided case, it does not coincide in general with the kernel (Davis and Maschler, Naval Res Logist Q 12:223–259, 1965). We also give an answer to an open question formulated by Rochford by introducing a kernel-based set whose intersection with the core coincides with the set of SMB.

Share functions for cooperative games with levels structure of cooperation

This discussion paper resulted in a publication in the European Journal of Operational Research , 2013, 224(1), 167-179. In a standard TU-game it is assumed that every subset of the player set can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure. In such games the player set is partitioned into unions and players can only cooperate within their own union. Owen introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one. A share function for TU-games is a type of solution that assigns to every game a vector whose components add up to one, and thus they can be interpreted as players shares in the worth to be allocated. Extending the approach to games with coalition structure developed by van den Brink and van der Laan (2005), we introduce a class of share functions for games with levels structure of cooperation by defining, for each player and each level, a standard TU-game. The share given to each player is then defined as the product of her shares in the games at every level. We show several desirable properties and provide axiomatic characterizations of this class of LS-share functions.

The Banzhaf value in the presence of externalities

We propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of these latter probability distributions, defined as the Banzhaf value of a coalitional game obtained as the expectation taken according to the given probability distributions of the original partition function form game. For each value of the family we provide two characterization results within the set of all partition function form games. Both results rely on a property of neutrality with respect to the amalgamation of players. Second, we propose another family of values that differ from the previous ones in that the latter values take into account only the information about the most likely coalition structure that may arise according to the given probability distributions. Each value of the second family is also characterized in two results by means of a collusion neutrality property. Unlike the characterizations of the first approach, these characterizations can be restricted to the set of simple games in partition function form.

The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets

We prove that both the nucleolus and the core-center, i.e., the mass center of the core, of an m-sided Böhm-Bawerk assignment market can be respectively computed from the nucleolus and the core-center of a convex game defined on the set of m sectors. What is more, in the calculus of the nucleolus of this latter game only singletons and coalitions containing all agents but one need to be taken into account. All these results simplify the computation of the nucleolus and the core-center of a multi-sided Böhm-Bawerk assignment market with a large number of agents. As a consequence we can show that, contrary to the bilateral case, for multi-sided Böhm-Bawerk assignment markets the nucleolus and the core-center do not coincide in general.

Costs of Change, Political Polarization, and Re-election Hurdles

We develop and study a two-period model of political competition with office- and policymotivated candidates, in which (i) changes of policies impose costs on all individuals and (ii) such costs increase with the magnitude of the policy change. We show that there is an optimal positive level of costs of change that minimizes policy polarization and maximizes welfare. One interpretation of this finding is that societies with intermediate levels of conservatism achieve the highest welfare and the lowest polarization levels. We apply our model to the design of optimal re-election hurdles. In particular, we show that raising the vote-share needed for re-election above 50% weakly reduces policy polarization and tends to increase welfare. Furthermore, we identify circumstances where the optimal re-election hurdle is strictly larger than 50%.

Channeling the final Say in Politics

We examine how the final say in a sequence of proposals for local public project provision, financing, and redistribution can be channeled towards socially desirable outcomes, thereby breaking the dictatorial power of the last agenda-setter. Individuals are heterogeneous with some citizens benefiting from the public project (winners) and the rest losing (losers) relative to per-capita costs. Our main insight is that a simple ban on subsidies for the proposal-makers can achieve the purpose whenever the first proposal-maker is a winner and the second proposal-maker is a loser. Such a ban induces project winners to make efficient public project proposals that are however coupled with socially undesirable subsidy schemes. The best possible amendment for project losers is then to match the project proposal and to eliminate all subsidies. We further show that two-round proposal-making constitutes the minimal form of political competition yielding first-best outcomes and that restrictions on tax schemes are socially desirable.

A Differential Redistributive Analysis of Bilinear Dual-Income-Tax Reforms

We analyze differential redistributive effects of bilinear tax reforms that are applied to dual income taxes or, more generally, to two different one-dimensional taxes. To do so we analyze the one-dimensional income tax case, and then we introduce a partial order, based on the Lorenz dominance criterion, which induces a lattice structure within the set of bilinear tax reforms whenever certain conditions on the tax reform policies and the dual income distribution hold. We illustrate this result empirically in the case of the Spanish dual personal income tax. We also analyze voting preferences and revenue elasticities, and we discuss the robustness of our theoretical predictions when some assumptions of the model are weakened.

Election Security and Economics: It’s All About Eve

A system’s security must be understood with respect to the capabilities and behaviors of an adversary Eve. It is often assumed in security analysis that Eve acts as maliciously as possible. From an economic perspective, Eve tries to maximize her utility in a game with other participants. The game’s rules are determined by the system and its security mechanisms, but Eve can invent new ways of interacting with participants. We show that Eve can be used as an interface to explore the interplay between security and economics in the domain of elections. Through examples, we illustrate how reasoning from both disciplines may be combined to explicate Eve’s motives and capabilities and how this analysis could be used for reasoning about the security and performance of elections. We also point to future research directions at the intersection of these disciplines.

From Hierarchies to Levels: New Solutions for Games

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure.