On ‘Nice’ and ‘Very Nice’ Autarkic Equilibria in Strategic Market Games*

Abstract

We study a strategic market game in which traders are endowed with both a good and money and can choose whether to buy or sell the good. We derive conditions under which a non‐autarkic equilibrium exists and when the only equilibrium is autarky. Autarky is ‘nice’ (robust to small perturbations in the game) when it is the only equilibrium, and ‘very nice’ (robust to large perturbations) when no gains from trade exist. We characterize economies where autarky is nice but not very nice, i.e. when gains from trade exist and yet no trade takes place.

An introduction to perfect and imperfect competition via bilateral oligopoly

“…Nevertheless, some existence results have been obtained in particular frameworks: Bonisseau and Florig (2003) proved the existence of a Cournot-Walras equilibrium in linear exchange economies; Codognato and Julien (2013) proved the existence in mixed exchange economies where agents on the continuum have Cobb-Douglas utility functions; and Shirai (2010) proves the existence of a Cournot-Walras equilibrium in production economies. 13 Bloch and Ferrer (2001a) and Dickson and Hartley (2013b) also consider the case in which agents are endowed with both commodities, i.e. have ''interior'' initial endowments, and can choose whether they become sellers or buyers.…”

Strategic trade in pollution permits

“…by Dickson and Hartley (2013)-that exploits the fact that firms' payoffs depend only on their own action and the aggregation of other firms' actions in B and Q, which themselves influence the price p. Here we present the reasoning for permit exchange coupled with subsequent product market decisions. The method allows the construction of supply and demand functions in the permit market that account for strategic behavior and endogenous formation of the sides of the market, and can be used to identify a permit market equilibrium.…”

On Cobb-Douglas Preferences in Bilateral Oligopoly

“…This issue was further investigated by Busetto and Codognato (2006) who considered whether autarky remained an equilibrium if any (not just small) external bids and offers are made to the market (in the same proportion), and coined it 'very nice' if so. Dickson and Hartley (2012) showed that autarky is nice if and only if it is the only equilibrium in the game, and very nice if and only if no gains from trade exist, and proceeded to consider whether there are economies in which autarky is nice but not very nice; that is, economies in which there are gains from trade but no trade takes place. This is an important question in bilateral oligopoly: as in Cournot competition the volume of trade is expected to be lower than a comparison with a competitive equilibrium, but does the fact that there are strategic traders on both sides of the market mean that trade may fail to take place at all?…”

“…A Shapley equilibrium (Shapley 1976) exists if either there is an equilibrium in which trade takes place, or autarky is very nice (see Busetto and Codognato (2006) or Dickson and Hartley (2012)). In a Cobb-Douglas economy the existence of a Shapley equilibrium is guaranteed.…”