Asymptotic expected number of Nash equilibria of two-player normal form games

The formula given by McLennan [The mean number of real roots of a multihomogeneous system of polynomial equations, Amer. J. Math. 124 (2002) 49–73] is applied to the mean number of Nash equilibria of random two-player normal form games in which the two players have M and N pure strategies respectively. Holding M fixed while N→∞, the expected number of Nash equilibria is approximately . Letting M=N→∞, the expected number of Nash equilibria is , where is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies.     

Deliberative monetary valuation (DMV): Issues in combining economic and political processes to value environmental change

This paper explores and contrasts the different social processes of valuation now appearing as economic means of valuing the environment. Monetary valuation via stated preference approaches has been criticised for assuming well formed and informed preferences and excluding a range of sustainability concerns such as rights, fairness and equity. Deliberative monetary valuation (DMV) in small groups is a novel hybrid of economic and political approaches which raises the prospect of a transformative and moralising experience. Critics of standard contingent valuation approaches have advocated this as offering a way forward. However there has been a lack of clarity as to the means of obtaining values, the expected outcomes and their role. Moving to group settings of deliberation raises concepts of social willingness to pay and accept which are distinct from an aggregate of individual value, although this does not seem to have been widely recognised. A new classification of values is presented appropriate to the literature trying to merge economic and political processes. Values associated with the individual may be exchange values, charitable contributions or fair prices, while social values can be speculative, expressive or arbitrated. The use of DMV is shown to result in different values due to variations in the institutional setting and process of valuation.