Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a "duality" axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dominance, and for gambles with normal distributions, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others in the literature. JEL classification: C00, C43, D00, D80, D81, E44, G00.

For games in partition function form, we explore the implications of distinguishing between the concepts of intrinsic marginal contributions and externalities. If one requires efficiency for the grand coalition, we provide several results concerning extensions of the Shapley value. Using the axioms of efficiency, anonymity, marginality and monotonicity, we provide upper and lower bounds to players' payoffs when affected by external effects, and a characterization of an ``externality-free'' value. If the grand coalition does not form, we characterize a payoff configuration on the basis of the principle of balanced contributions. We also analyze a game of coalition formation that yields sharp predictions Keywords:. externalities, marginal contributions, Shapley value, Pigouvian transfers, coalition formation JEL classification:. C7, D62 Abstract For games in partition function form, we explore the implications of distinguishing between the concepts of intrinsic marginal contributions and externalities. If one requires efficiency for the grand coalition, we provide several results concerning extensions of the Shapley value. Using the axioms of efficiency, anonymity, marginality and monotonicity, we provide upper and lower bounds to players' payoffs when affected by external effects, and a characterization of an "externality-free" value. If the grand coalition does not form, we characterize a payoff configuration on the basis of the principle of balanced contributions. We also analyze a game of coalition formation that yields sharp predictions. JEL classification numbers: C7, D62

We study a multilateral bargaining procedure that extends Rubinstein's alternating offer game to the case of n players. The procedure captures the notion of consistency in the sense familiar in cooperative game theory and we use it to establish links to the axiomatic theory of bargaining. 61 1. Lensberg (1988) uses the term "stability". We use the term consistency in order to be, well, consistent with similar usage in cooperative game theory.

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We analyse a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and efficiency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is two-sided or one-sided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steadystate equilibria of a model where agents enter the market every period.

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Consider any investor who fears ruin when facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure α is more informative than information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.