Information in Tullock contests

In Tullock contests in which the common value of the prize is uncertain and the elasticity of the marginal cost of effort is increasing (decreasing), the effect of changes of players’ information on the equilibrium efforts and payoffs is unambiguous: if information is symmetric, then expected effort decreases (increases) as players become better informed; in two-player contests, the expected effort of a player with information advantage is less (greater) than that of his opponent. Sharper results arise when the cost of effort is linear: Under symmetric information, expected effort and payoff are invariant to changes in the players’ information. In two-player contests, both players exert the same expected effort regardless of their information, although expected effort is smaller when one player has information advantage than when both players have the same information. Interestingly, the expected payoff of a player with information advantage is larger than that of his opponent, even though he wins the prize less frequently.Acknowledgments of financial support: Israel Science Foundation, Grant 648/2 (Einy); Ministerio Economía (Spain), Grants ECO2014-55953-P and MDM2014-0431, and Comunidad de Madrid, Grant S2015/HUM-3444 (Moreno)

A probabilistic unified approach for power indices in simple games

The final publication is available at Springer via https://doi.org/10.1007/978-3-662-60555-4_11Many power indices on simple games have been defined trying to measure, under different points of view, the “a priori” importance of a voter in a collective binary voting scenario. A unified probabilistic way to define some of these power indices is considered in this paper. We show that six well-known power indices are obtained under such a probabilistic approach. Moreover, some new power indices can naturally be obtained in this way.Peer ReviewedPostprint (author's final draft

Correlation and Inequality in Weighted Majority Voting Games

In a weighted majority voting game, the weights of the players are determined based on some socio-economic parameter. A number of measures have been proposed to measure the voting powers of the different players. A basic question in this area is to what extent does the variation in the voting powers reflect the variation in the weights? The voting powers depend on the winning threshold. So, a second question is what is the appropriate value of the winning threshold? In this work, we propose two simple ideas to address these and related questions in a quantifiable manner. The first idea is to use Pearson's Correlation Coefficient between the weight vector and the power profile to measure the similarity between weight and power. The second idea is to use standard inequality measures to quantify the inequality in the weight vector as well as in the power profile. These two ideas answer the first question. Both the weight-power similarity and inequality scores of voting power profiles depend on the value of the winning threshold. For situations of practical interest, it turns out that it is possible to choose a value of the winning threshold which maximises the similarity score and also minimises the difference in the inequality scores of the weight vector and the power profile. This provides an answer to the second question. Using the above formalisation, we are able to quantitatively argue that it is sufficient to consider only the vector of swings for the players as the power measure. We apply our methodology to the voting games arising in the decision making processes of the International Monetary Fund (IMF) and the European Union (EU). In the case of IMF, we provide quantitative evidence that the actual winning threshold that is currently used is sub-optimal and instead propose a winning threshold which has a firm analytical backing. On the other hand, in the case of EU, we provide quantitative evidence that the presently used threshold is very close to the optimal

Full vs Partial Market Coverage with Minimum Quality Standards

The consequences of the adoption of quality standards on the extent of market coverage is investigated by modelling a game between regulator and low-quality firm in a vertically differentiated duopoly. The game has a unique equilibrium in the most part of the parameter range. There exists a non-negligible range where the game has no equilibrium in pure strategies. This result questions the feasibility of MQS regulation when firms endogenously determine market coverage

Restricted Coalition Formation

Very often in social life individuals take decisions within groups (households, friendships, trade unions, local jurisdictions, networks, etc.). The formation of coalition may imply some theoretical difficulties, such as costs arising from forming a coalition or sharing information among agents. Coalition formation has the explicit purpose to represent the process of formation of coalitions of agents and hence modelling a number of relevant economic and social phenomena. Moreover, following this theoretical and applied literature on coalitions, the seminal chapter by Jackson and Wolinsky (1996) opened the way to a new stream of contributions using networks (graphs) to model the formation of links among individuals. In this chapter we will assume that only a subset S of the set of all possible coalitions in an economy is the set of admissible coalitions. We define the S -core concept, as in Hervès-Moreno. We will extend to a model with both uncertainty and asymmetric informations the results showed in Okuda and Shitovitz