Embedded Files
I) Political Economy
I.1) General
25. Gersbach, H., Mamageishvili, A., Tejada, O. (2020). Appointed Learning for the Common Good: Optimal Committee Size and Efficient Reward. Submitted.
Abstract: A population of identical individuals must choose one of two alternatives under uncer- tainty about what the right alternative is. Individuals can gather information of increasing accuracy at an increasing convex utility cost. For such a setup, we analyze how vote del- egation to a committee and suitable monetary transfers for its members can ensure that high or optimal levels of information are (jointly) acquired. Our main insight is that to maximize the probability of choosing the right alternative committee size must be small, no matter whether information acquisition costs are private or not. Our analysis and results cover two polar cases—information costs are either private or public--and unravel both the potential and the limitations of monetary transfers in committee design.
Full paper: Working paper
22. Gersbach, H., Mamageishvili, A., Tejada, O. (2019). The Market for Lemons with Seller Partition. Submitted.
Abstract: We introduce a four-stage, multi-prize buying mechanism, which can be used by a (big) buyer to separate low-quality sellers---called ``lemon'' owners---from high-quality sellers. When the pool of sellers can be partitioned into groups with known mixes of high- and low-quality sellers, the buyer obtains the commodities from the high-quality sellers at a price that matches the willingness to sell. By contrast, ''lemon'' owners are trapped into selling their items at a low, or even negligible, price. These properties hold even if the buyer cannot commit to a single execution of the mechanism. We outline some applications of our results and suggest that our mechanism might be useful for market makers.
Full paper: Working paper
13. Gersbach, H., Schneider, M., Tejada, O. (2017). Coalition-Preclusion Contracts and Moderate Policies. Games and Economic Behavior.
Abstract: We examine the effects of a novel political institution, which we call Coalition-Preclusion Contracts, on elections, policies, and welfare. Coalition-Preclusion Contracts enable political parties to credibly commit before the elections not to form a coalition after the elections with one or several other parties specified in the contract. We consider a political game in which three parties compete to form the government and study when contracts of the above type will be written. We find that in most circumstances Coalition-Preclusion Contracts with a single-party exclusion rule defend the interests of the majority by moderating the policies implemented. Moreover, they yield welfare gains for a large set of parameter values. We discuss the robustness of the results in more general settings and study how party-exclusion rules have to be adjusted when more than three parties compete in an election.
Full paper: Publisher, Working Paper
I.2) Electoral Competition
24. Gersbach, H., Jackson, M., P., Tejada, O. (2020). The Optimal Length of Political Terms. Submitted
Abstract: We analyze the optimal length of political terms (equivalently, the optimal frequency with which elections should be held) when the candidates of two polarized parties compete for office and the median voter shifts over time. Office-holders determine policy and experience persistent random shocks to their valence. Policy changes are costly for citizens and politicians. Optimal term-length balances the frequency of costly policy changes when parties change office with the incumbent's average valence during tenure. We fi nd that optimal term-length increases with party polarization, with the degree to which the median voter cares about valence, and with the frequency and the size of swings in the electorate. In contrast, optimal term-length decreases when candidates for office undergo less scrutiny or when parties care more about future outcomes. Finally, with small swings in the electorate and large polarization, optimal term-length increases if checks and balances increase.
Full paper: Working Paper
23. Gersbach, H., Jackson, M., Muller, P., Tejada, O. (2020). Electoral Competition with Costly Policy Changes: A Dynamic Perspective. Submitted
Abstract: We analyze dynamic electoral competition policy changes. The costs of changing a policy increase with the extent of the shift and generate an incumbency advantage. We characterize the dynamics of Markov equilibria in terms of history and party polarization, and analyze how policies are influenced by the amplitude and convexity of costs of change, as well as by the degree of party and voter farsightedness. Regardless of the initial policy, party choices converge in the long run to a stochastic alternation between two (regions of) policies, with transitions occurring when office-holders su er a shock to their capacity or valence. Although costs of change have a moderating effect on policies, full convergence to the median voter position does not take place.
Full paper: Working Paper
16. Gersbach, H., Tejada, O. (2017). The Reform Dilemma in Polarized Democracies. Journal of Public Economics.
Abstract: We study the feasibility and efficiency of policy reforms in polarized democracies. We develop a simple election model where (i) reforms are costly for voters and politicians and these costs increase with the extent of policy change, and (ii) politicians differ in their ability to carry out reforms efficiently. We identify a so-called Reform Dilemma, which manifests itself in two variants. From a static perspective, low-reform-ability politicians may be elected, who impose high costs on citizens for each reform step. From a dynamic perspective, incumbents may choose socially undesirable policies to align the social Need for reform with their own reform ability and are thus re-elected regardless of their Reform ability. In general, both manifestations of the Reform Dilemma are more pronounced when political parties’ positions are polarized. Furthermore, the existence of the Reform Dilemma is independent of the exact point in time when the abilities of candidates reveal themselves and become common knowledge.
Full paper: Publisher, Working Paper
14. Gersbach, H., Muller, P., Tejada, O. (2019). The Effects of Costs of Change on Political Polarization. Accepted in European Journal of Political Economy.
Abstract: We study a two-period model of policy-making where (i) changes of current policies impose costs on all individuals that increase linearly with the magnitude of the policy shift and (ii) political power changes over time. We show that policy polarization is minimal for intermediate marginal costs. In turn, welfare is a single-peaked function of the marginal cost. One interpretation is that societies with political institutions that impose positive but moderate costs on political reforms simultaneously achieve the highest welfare and the lowest policy polarization.
Full paper: Publisher, Working Paper
I.3) Voting
21. Gersbach, H., Mamageishvili, A., Tejada, O. (2017). The Effect of Handicaps on Turnout for Large Electorates: An Application to Assessment Voting. Revision Requested at Journal of Economic Theory.
Abstract: We analyze the effect of handicaps on turnout. A handicap is a difference in the vote tally between alternatives that strategic voters take as predetermined when they decide whether to turn out for voting. Handicaps are implicit in many existing democratic procedures. Within a costly voting framework with private values, we show that turnout incentives diminish considerably across the board if handicaps are large, while low handicaps yield more mixed predictions. The results extend beyond the baseline model - e.g. by including uncertainty and behavioral motivations - and can be applied to the optimal design of Assessment Voting. This is a new voting procedure where (i) some randomly-selected citizens vote for one of two alternatives, and the results are published; (ii) the remaining citizens vote or abstain, and (iii) the final outcome is obtained by applying the majority rule to all votes combined. If the size of the first voting group is appropriate, large electorates will choose the majority's preferred alternative with high probability and average participation costs will be moderate or low.
Full paper: Working Paper
18. Gersbach, H., Tejada, O. (2017). Semi-Flexible Majority Rules for Public Good Provision. Submitted.
Abstract: We introduce a two-stage, multiple-round voting procedure where the thresholds needed for approval require a qualified majority and vary with the proposal on the table. We apply such a procedure to instances of public-good provision where the citizens’ valuations can take two values and are private. We show that the procedure elicits and aggregates the information about the valuations and implements the utilitarian optimal public good level. This level is chosen after all potential socially optimal policies have been considered. We also develop a compound procedure to ensure utilitarian optimality when there are arbitrarily finitely many types of citizen.
Full paper: Working paper
8. Gersbach, H., Imhof, S., Tejada, O. (2017). Channeling the Final Say in Politics: A Simple Mechanism. Accepted at Economic Theory.
Abstract: We examine project provision and redistribution in a model of legislative bargaining, and provide a foundation of how to channel the say when complete social contracts are not enforceable. We consider a large and heterogeneous legislature and show that socially optimal outcomes are obtained by a mechanism based on the majority rule that involves two proposal-making rounds, with the minority moving first and the majority moving second.
Full paper:
II) (Cooperative) Game Theory
II.1) General
20. Tejada, O., Álvarez-Mozos, M (2017). Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus. Mathematical Social Sciences.
Abstract: We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new values extending the Shapley value and the Banzhaf value, respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in today's fully integrated societies.
Full paper: Publisher, Working paper
15. Álvarez-Mozos, M., van den Brink, R., van der Laan, G, Tejada, O. (2015). From Hierarchies to Levels: New Solutions for Games with Hierarchical Structure. International Journal of Game Theory, 46(4), 1089-1113.
Abstract: 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.
Full paper: Publisher, Working paper
12. Álvarez-Mozos, M., Tejada, O. (2015). The Banzhaf Value in the Presence of Externalities. Social Choice and Welfare, 44(4), 781–805.
Abstract: 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.
Full paper: Publisher, Working Paper
7. Álvarez-Mozos, M., van den Brink, R., van der Laan, G, Tejada, O. (2013). Share functions for cooperative games with levels structure of cooperation. European Journal of Operational Research, 224(1), 167-179.
Abstract: In a standard TU-game it is assumed that every subset of the player set N can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered are games with coalition structure of Aumann (1974). They assumed that the player set is partitioned into unions and that players can only cooperate within their own union. Owen (1977) introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter (1989) 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 which 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 in 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.
Full paper: Publisher, Working paper
4. Álvarez-Mozos, M., Tejada, O. (2011). Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with levels structure of cooperation. Decision Support Systems, 52(1), 21-27.
Abstract: 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 by Winter(1989), 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 in terms of easily comparable sets of properties and we illustrate them by means of an example.
Full paper: Publisher, Working paper
II.2) Assignment Games (and Related Topics)
11. Tejada, O., Borm, P., Lohmann, E. (2013). A Unifying Model for Matrix-based Pairing Situations. Mathematical Social Sciences, 2014(72), 55-61.
Abstract: We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called pairing games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a pairing game is always nonempty by proving that the set of pairing games coincides with the set of permutation games. Then we exploit the wide range of situations comprised in our framework to investigate the relationship between pairing games with different player sets but defined by the same underlying matrix. We show that the core and the set of extreme core allocations are immune to the merging of a row player and a column player. Moreover, the core is also immune to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general.
Full paper: Publisher, Working Paper
10. Tejada, O., Álvarez-Mozos, M.(2016). Vertical Syndication-Proof Competitive Prices in Multilateral Markets. Review of Economic Design, 20(4),289-327.
Abstract: We consider a market comprising a number of perfectly complementary and homogeneous commodities. We concentrate on the incentives for firms producing these commodities to merge and form a vertical syndicate. The main result establishes that the nucleolus of the associated market game corresponds to the unique vector of prices with the following properties: (i) they are vertical syndication-proof, (ii) they are competitive, (iii) they yield the average of the buyers- and the sellers-optimal allocations in bilateral markets, and (iv) they depend on the traders’ bargaining power but not on their identity. The proof uses an isomorphism between our class of market games and the entire class of bankruptcy games.
Full paper: Publisher, Working paper
9. Tejada, O. (2013). Complements and Substitutes in General Multisided Assignment Economies. Operations Research Letters 41(5), 468-473.
Abstract: We consider a finitely populated economy in which there are different types of agent, each agent is of one type, and profit is created by coalitions containing at most one agent of each type. We present negative results establishing that agents of different type may not be complements and agents of the same type may not be substitutes. We propose novel notions for the complementarity and substitutability of disjoint coalitions, and we find conditions under which they hold.
Full paper: Publisher, Working paper (with extra material)
6. Tejada, O., Núñez, M. (2012). Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center. Mathematical Methods of Operations Research, 75(2), 199-220.
Abstract: We show that, contrary to the bilateral case, for multi-sided Böhm-Bawerk assignment markets the nucleolus and the core-center, i.e. the mass center of the core, do not coincide in general. To do so, we prove that both the nucleolus and the core-center 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. Even 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. These results simplify the computation of the nucleolus of a multi-sided Böhm-Bawerk assignment market with large number of agents.
Full paper: Publisher, Working paper
3. Tejada, O. (2013). Analysis of the core of multisided Böhm-bawerk assignment markets. TOP, 21(1), 189-205.
Abstract: We introduce the class of multisided Böhm-Bawerk assignment games which generalizes the well-known two-sided Böhm-Bawerk assignment games to markets with an arbitrary number of sectors. We reach the core and the corresponding extreme allocations of any multisided Böhm-Bawerk assignment game by means of an associated convex game defined on the set of sectors instead of the set of sellers and buyers. We also study when the core of a multisided Böhm-Bawerk assignment game is stable in the sense of von Neumann–Morgenstern.
Full paper: Publisher, Working paper
2. Tejada, O. (2010). A note on competitive prices in multilateral assignment markets. Economics Bulletin, 30(1), 658-662.
Abstract: A multilateral assignment market with buyers and a number of different types of firms can be modeled by a multi-sided assignment game. We prove that core allocations of the latter are in a one-to-one correspondence with competitive prices of the former, where the notion of competitive price extends that of Roth and Sotomayor (1990). This result generalizes to multi-sided assignment markets the characterization of competitive prices known for the two-sided case.
Full paper: Publisher
1. Tejada, O., Rafels, C. (2010). Symmetrically multilateral-bargained allocations in multi-sided assignment markets. International Journal of Game Theory, 39(2), 249-258.
Abstract: 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.
Full paper: Publisher, Working paper
II.3) Bargaining
17. Grech, P., Tejada, O. (2016). Divide the Dollar and Conquer More: Sequential Bargaining and Risk Aversion. Forthcoming in International Journal of Game Theory.
Abstract: We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash Bargaining Solution (NBS). For one-shot negotiations, a cornerstone result of \cite{roth_risk_1989} establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs along several rounds. In each round, only a share of the total amount is negotiated over according to the NBS, with the disagreement point being determined by the outcome of the previous rounds. In accordance with Roth's result, the amount received by the more risk averse player is still bounded by half the total amount. In addition, this player does not lose from bargaining over more rounds if his opponent exhibits non-increasing absolute risk aversion. Finally, both players' risk profiles become essentially irrelevant if the number of rounds is sufficiently large.
Full paper: Publisher, Working paper
III) Public Economics
5. Calonge, S., Tejada, O. (2011). A differential redistributive analysis of bilinear tax reforms. FinanzArchiv: Public Analysis, 67(3), 193-224.
Abstract: 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.
Full paper: Publisher
IV) Other papers
19. Basin, D, Gersbach, H., Mamageishvili, A., Schmid, L., Tejada, O. (2017). Election Security and Economics: It’s all about Eve. Forthcoming in 2nd International Joint Conference on Electronic Voting (evoteID).
Abstract: 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.
Full paper: Working paper
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