Group Contests with Complementarities in Efforts

Usually, groups increase their productivity by the specialization of their group members. In these cases, group output is no longer simply a sum of individual outputs. We analyze contests with group-specific public goods that allow for different degrees of complementarity between group members’ efforts. More specifically, we use a Tullock contest success function and a CES-impact function. We show that in equilibrium the degree of complementarity is irrelevant if groups do not differ in size and group members have an identical valuation of the public good. The equilibrium is discontinuous as the CES function converges to the Cobb-Douglas case. Except for the effects at the discontinuity, higher complementarity tends to favor larger groups. In groups with diverse valuations, higher complementarity also leads to higher similarity in group members’ efforts, which however is not necessarily an advantage for a more diverse group.contests, public goods

Technological Determinants of the Group-Size Paradox

The present paper analyzes situations in which groups compete for rents. A major result in the literature has been that there are both cases where larger groups have advantages and cases where they have disadvantages. The paper provides two intuitive criteria which for groups with homogenous valuations of the rent determine whether there are advantages or disadvantages for larger groups. For groups with heterogenous valuations the complementarity of group members’ efforts is shown to play a role as a further factor.contests, public goods, group-size paradox

Procedural Mixture Spaces

This paper provides a representation theorem for procedural mixture spaces. Procedural mixture spaces are mixture spaces in which it is not necessarily true that a mixture of two identical elements yields the same element. Under the remaining standard assumptions of mixture spaces, the following representation theorem is proven; a rational, independent, and continuous preference relation over mixture spaces can be represented either by expected utility plus the Shannon entropy or by expected utility under probability distortions plus the Renyi entropy. The entropy components can be interpreted as the utility or disutility from resolving the mixture and therefore as a procedural as opposed to consequentialist value

Procedural Mixture Spaces

This paper provides a representation theorem for procedural mixture spaces. Procedural mixture spaces are mixture spaces in which it is not necessarily true that a mixture of two identical elements yields the same element. Under the remaining standard assumptions of mixture spaces, the following representation theorem is proven; a rational, independent, and continuous preference relation over mixture spaces can be represented either by expected utility plus the Shannon entropy or by expected utility under probability distortions plus the Renyi entropy. The entropy components can be interpreted as the utility or disutility from resolving the mixture and therefore as a procedural as opposed to consequentialist value

Measuring Freedom in Games

Behind the veil of ignorance, a policy maker ranks combinations of game forms and information about how players interact within the game forms. The paper presents axioms on the preferences of the policy maker that are necessary and sufficient for the policy maker's preferences to be represented by the sum of an expected valuation and a freedom measure. The freedom measure is the mutual information between players' strategies and the players' outcomes of the game, capturing the degree to which players control their outcomes. The measure extends several measures from the opportunity set based freedom literature to situations where agents interact. This allows freedom to be measured in general economic models and thus derive policy recommendations based on the freedom instead of the welfare of agents. To illustrate the measure and axioms, applications to civil liberties and optimal taxation are provided

Conditionally Additive Utility Representations

Advances in behavioral economics have made decision theoretic models increasingly complex. Utility models incorporating insights from psychology often lack additive separability, a major obstacle for decision theoretic axiomatizations. We address this challenge by providing representation theorems which yield utility functions of the form u(x,y,z)=f(x,z) + g(y,z). We call these representations conditionally separable as they are additively separable only once holding fixed z. Our representation theorems have a wide range of applications. For example, extensions to finitely many dimensions yield both consumption preferences with reference points Sum_i u_i(x_i,r), as well as consumption preferences over time with dependence across time periods Sum_t u_t(x_t,x_{t-1})