Endogenous participation costs and equilibrium abstention in voting with complete information: A three-player case

This note examines the endogenous determination of participation costs in a costly voting game with complete information when there are three voters. I Â…find that there are two types of equilibria: (1) one where a voter who has a minority opinion definitely abstains, and (2) where he or she votes with some positive probability. In either equilibrium, the voter never invests to reduce his or her participation costs. Thus, inefficiency arises solely from a free-rider problem among voters in the majority.Voting, Endogenous participation costs

Costly participation in voting and equilibrium abstention: a uniqueness result

This note shows that a unique mixed Nash equilibrium obtains when there are three voters in Palfrey and Rosenthal's (1983) costly voting game under complete information. Experimental investigation of this result might be interesting.Abstention

Ministerial Weights and Government Formation: Estimation Using a Bargaining Model

This paper proposes a method to estimate relative ministerial weights in parliamentary democracies. Specifically, our method combines a bargaining model of government formation with maximum likelihood estimation. The data required for estimation are who formateurs are, what each party’s voting weight is, and what ministerial seats each party obtains. We use variation of the data and the structure of the bargaining model to recover ministerial weights and other parameters. Additionally, the method can measure the effects of voting weights and formateur advantage. We apply our proposed method to the case of Japan. Our results statistically show that political players value pork-related posts (such as the Minister of Construction) more than prestigious ones (such as the Minister of Foreign Affairs). We also find that there is a significant formateur advantage, while voting weights do not have a significant scale effectGovernment Formation, Bargaining

The Welfare Effects of Third-Degree Price Discrimination in a Differentiated Oligopoly

This paper studies the relationship between horizontal product differentiation and the welfare effects of third-degree price discrimination in oligopoly. By deriving linear demand from a representative consumer's utility and focusing on the symmetric equilibrium of a pricing game, we characterize the conditions relating to such demand properties as substitutability and complementarity for price discrimination to improve social welfare. In particular, we show that price discrimination can improve social welfare if firms' brands are substitutes in a market where the discriminatory price is higher and complements in one where it is lower, but welfare never improves in the reverse situation. We verify, however, that consumer surplus is never improved by price discrimination; welfare improvement by price discrimination is solely due to an increase in the firms' profits. This means that there is no chance that firms suffer from a "prisoners' dilemma," that is, firms are better off by switching from uniform pricing to price discrimination.

A Category of Probability Spaces

We introduce a category \Prob of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement. We can consider a \Prob-arrow as an evolving direction of information. We introduce a contravariant functor $\mathcal{E}$ from \Prob to \Set, the category of sets. The functor $\mathcal{E}$ provides conditional expectations along arrows in \Prob, which are generalizations of the classical conditional expectations. For a \Prob-arrow $f^-$, we introduce two concepts $f^-$-measurability and $f^-$-independence and investigate their interaction with conditional expectations along $f^-$. We also show that the completion of probability spaces is naturally formulated as an endofunctor of \Prob

The Welfare Effects of Third-Degree PriceDiscrimination in a Differentiated Oligopoly

This paper studies the welfare effects of third-degree price discrimination under oligopolistic competition with horizontal product differentiation. We derive a necessary and sufficient condition for price discrimination to improve social welfare: the degree of substitution must be sufficiently greater in the "strong" market (where the discriminatory price is higher than the uniform price) than in the "weak" market (where it is lower). It is verified, however, that consumer surplus is never improved; social welfare improves solely due to an increase in the firms' profits.Third-degree price discrimination, Oligopoly, Social welfare, Horizontal product differentiation, Substitutability, Complementarity