Exponential Utility Function

Stochastic Contests with Linex Utility Functions

Öz:

In this paper, we analyze the Nash equilibrium in a class of winner-takes-all stochastic contests among players with linearexponential (linex) utility functions. In this contest, players are required to make upfront investments, which collectivelydetermine their winning probabilities. We first show that a Nash equilibrium for such a contest exists and is unique, then set theequilibrium conditions, and study the properties of these conditions to gain insights into the structure of equilibrium. We showthat the total equilibrium investment is bounded below and above, that the equilibrium has a cut characterization with respectto wealth, and that wealthier players invest more. The latter implies that richer is likely to get richer. For the special case withidentical players, we show that an increase in the wealth or a decrease in the weight on the nonlinear component of the linexutility function results in an increase in the equilibrium investment.

Anahtar Kelime:

This paper analyzes the information acquisition problem in a two-action lottery setting. Information is evaluated using the buying price approach. We investigate the relationship between risk aversion and the value of information in the case of two one-switch utility function families: sumex, and linear plus exponential utility. We derive conditions under which there exists a monotonic relationship between the decision maker’s risk tolerance and the value of information.

 

Bu makale iki seçenekli lotarya kararı verilen bir ortamda bilgi edinimi problemini ele almaktadır. Bilginin değeri alış fiyatı yaklaşımı ile hesaplanmıştır. Yaptığımız çalışmada riske duyarlılık ile bilginin değeri arasındaki ilişkiyi iki farklı tek değişimli fayda fonksiyonu ailesini kullanarak inceledik. Üzerinde çalışılan tek değişimli fayda fonksiyonu aileleri de sumex ve doğrusal artı üssel fayda fonksiyonu aileleridir. Bu bağlamda karar vericinin riske duyarlılığı ve bilginin değeri arasında hangi koşullar altında monotonik bir ilişki olduğu ortaya çıkarılmıştır.