We analyze a non-cooperative game in which the set of feasible strategy profiles is compact and convex but possibly non-rectangular. Thus, a player's feasible strategies may depend on the strategies used by others, as in Debreu's (1952, 1982) generalized games. In contrast to the model of Debreu, we do not require preferences to be defined over infeasible strategy profiles, and we do not requir...

We model the exchange of commodities that are contingent upon each other when traders place mostly limit orders Examples include a market of nancial futures where future spreads are also traded a market of mutual funds and stocks a market of options and stocks under the viewpoint that they are both combinations of Arrow Debreu securities We prove that consistent prices are optimal We develop a ...

We begin by looking at a set of theorems from various disciplines and how they relate to one another. From combinatorics, we take Sperner’s Lemma which we can use to prove Brouwer’s Fixed Point Theorem from topology. Brouwer’s Fixed Point Theorem can be used to prove the Arrow-Debreu Theorem from economics which states that general equilibria exist, and can also be used to prove Kakutani’s Fixe...

Catastrophic risks are rare events with major consequences, e.g. catastrophic climate change or extinction of a species. The article summarizes decision theory involving catastrophic risks within Von Neumann’s axiomatic theory of choice under uncertainty, and within new extensions of the theory that are speci…cally designed for rare events of major consequences. The classic expected utility the...

Two Arrow–Debreu market games are formulated whose straightforward Nash equilibria are Walrasian. Both have an auctioneer setting prices to maximize net sales value. In the second an additional redistributive agency maximizes welfare through optimal lump-sum transfers. In intertemporal economies, however, subgame imperfections can arise because agents understand how current decisions such as th...

This paper studies the equilibrium property and algorithmic complexity of the exchange market equilibrium problem with more general utility functions: piece-wise linear functions, which include Leontief’s utility functions. We show that the Fisher model again reduces to the general analytic center problem, and the same linear programming complexity bound applies to approximating its equilibrium...

The overlapping expectations and the collective absence of arbitrage conditions introduced in the economic literature to insure existence of Pareto optima and equilibria with short-selling when investors have a single belief about future returns, is reconsidered. Investors use measures of risk. The overlapping sets of priors and the Pareto equilibrium conditions introduced by Heath and Ku for c...

In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu-Gale-Nikaido type theorem, with a considerable weakned W...

We examine whether economies constructed using experimentally measured preferences (for risk) tend to suffer from aggregation pathologies (like nonexistence and multiplicity of equilibrium) cautioned by the Sonnenschein–Mantel–Debreu theorem. show that should be expected arise frequently in homogeneous exchange economies, but dwindle eventually disappear as grow diverse. When subjects actually ...