An individual that follows partial Kantian universalization polarizes and overdraws its strategy in order to compensate for those individuals that she thinks do not choose the same strategy as she does. Within a generalized Alger-Weibull approach with heterogenous homo moralis individuals, the present paper is the first to formalize this polarization incentive. We show that the polarization incentive can be drawn back to an implicit and so far unknown ’preference for dominance’. Applying our new insights to a public good game it turns out that total public good provision may be reduced by an increase in the degree of morality.
We justify the prevalence of small reserve prices in real-life auctions despite empirical findings that suggest optimal reserve prices in those contexts should be higher. We reconcile such a discrepancy without modifying the standard assumptions about bidders’ preferences, information, or the market environment. Instead, we introduce a form of uncertainty on the seller’s side regarding the distribution of valuations. This uncertainty may arise when the bid sample lacks variables necessary to determine the valuation distribution or when its point estimate differs from the true distribution. We show that the optimal reserve price under uncertainty decreases as the number of bidders grows, and the revenue gain from the optimal reserve price relative to any smaller reserve price—including zero—disappears at an exponential rate. We then show that the reserve price decreases further as the amount of uncertainty, as represented by the integrated variance of the valuation distributions, increases. Finally, we extend the analysis to a risk-averse seller and show that risk aversion reinforces the effect of uncertainty, further lowering the optimal reserve price as the seller trades off expected revenue against revenue volatility.
This paper axiomatically characterizes the rule of aggregating individuals’ ambiguous beliefs into the society’s ambiguous belief. We consider a family of social rankings over acts which are indexed by pairs of utility profiles and ambiguous belief profiles, and impose variable-profile axioms which express how society should respond to changes in belief profiles and changes in how beliefs disagree. Our characterization allows two kinds of collective ambiguity aversion, one arising due to individuals’ ambiguity aversion and the other arising due to disagreements in beliefs.
This paper introduces the notion of 𝒢 -rules, which extend the Pareto rule when populations are endogenous. Societal evaluations of lives are required. 𝒢 -rules compare pairs of allocations whenever evaluating the gains of some agents—utility gains or benefits of (not) being born—against the losses of others is not required. 𝒢 -efficiency naturally arises. The 𝒜 and 𝒫 criteria of Golosov et al. (2007) are special cases. Transitive 𝒢 -rules admit an axiomatic foundation based on normatively appealing properties and can be conveniently represented with 𝒢 -nondecreasing critical levels. Many public policies that distort fertility decisions are 𝒢 -efficient because they benefit children who are (not) born as a result of these policies.
Largesse design is a positive theory of what happens when players in a game, who have a limited willingness to sacrifice for the common good, can coordinate on a welfare-optimal solution. This theory provides an alternative to psychological theories in explaining why players engage in costly punishments and rewards. It also says that players will engage in other low-cost methods of encouraging pro-social behavior, for example, through reputation effects. In this paper, I study the properties and comparative statics of the largesse design problem. Despite a lack of concavity in the maximization problem, solutions are unique and continuous except on a lower-dimensional bifurcation set. In examples, I study these bifurcations, in which a small change in the parameters can lead to a large change in behavior or welfare.
