Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer setting bid and ask prices nearly equal to Walrasian equilibrium prices. In the model agents trade either through the intermediary or privately. Buyers (sellers) choosing to trade through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as potential gains. Agents trading privately capture all of the gains to trade, but risk costly delay in finding a partner. We show that when the cost of delay is small, the intermediary sets bid and ask prices nearly equal to Walrasian equilibrium prices. As the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. If the possibility of trading through the intermediary is removed, and therefore all trade takes place in the private trading market, then prices are not close to Walrasian equilibrium prices even as the cost of delay vanishes

Bargaining and matching in small markets

The present paper focuses on markets where trade is carried out through matching and bargaining and where at each date t = 0,1, ... a finite and exogenously given number of agents enters. Such markets are "small" in the sense that whether a match ends with trade influences matching probabilities at subsequent dates. For a small market we show that as the market becomes large, the equilibrium of the small market converges to the equilibrium of a limit market with a continuum of agents. Nonetheless, for any small market there exists a matching process such that the equilibrium of the small market significantly differs from the equilibrium of the associated large market with a continuum of agents, although equilibrium-path matching probabilities are the same in both markets. Therefore, matching models with a continuum of agents are not always a good approximation of small markets

Equilibrium in a market with intermediation is Walrasian.

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer setting bid and ask prices nearly equal to Walrasian equilibrium prices. In the model agents trade either through the intermediary or privately. Buyers (sellers) choosing to trade through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as potential gains. Agents trading privately capture all of the gains to trade, but risk costly delay in finding a partner. We show that when the cost of delay is small, the intermediary sets bid and ask prices nearly equal to Walrasian equilibrium prices. As the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. If the possibility of trading through the intermediary is removed, and therefore all trade takes place in the private trading market, then prices are not close to Walrasian equilibrium prices even as the cost of delay vanishes.Intermediation; Walrasian equilibrium; Matching; Bargaining;

Market games and clubs

The equivalence of markets and games concerns the relationship between two sorts of structures that appear fundamentally different -- markets and games. Shapley and Shubik (1969) demonstrates that: (1) games derived from markets with concave utility functions generate totally balanced games where the players in the game are the participants in the economy and (2) every totally balanced game generates a market with concave utility functions. A particular form of such a market is one where the commodities are the participants themselves, a labor market for example. But markets are very special structures, more so when it is required that utility functions be concave. Participants may also get utility from belonging to groups, such as marriages, or clubs, or productive coalitions. It may be that participants in an economy even derive utility (or disutility) from engaging in processes that lead to the eventual exchange of commodities. The question is when are such economic structures equivalent to markets with concave utility functions. This paper summarizes research showing that a broad class of large economies generate balanced market games. The economies include, for example, economies with clubs where individuals may have memberships in multiple clubs, with indivisibile commodities, with nonconvexities and with non-monotonicities. The main assumption are: (1) that an option open to any group of players is to break into smaller groups and realize the sum of the worths of these groups, that is, essential superadditivity is satisfied and :(2) relatively small groups of participants can realize almost all gains to coalition formation. The equivalence of games with many players and markets with many participants indicates that relationships obtained for markets with concave utility functions and many participants will also hold for diverse social and economic situations with many players. These relationships include: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or approximate cores; (c) the equal treatment property holds -- that is, both market equilibrium and the core treat similar players similarly. These results can be applied to diverse economic models to obtain the equivalence of cooperative outcomes and competitive, price taking outcomes in economies with many participants and indicate that such results hold in yet more generality.Markets; games; market games; clubs; core; market-game equivalence; Shapley value; price taking equilibrium; small group effectiveness; inessentiality of large groups; per capita boundedness; competitive equilibrium; games with side payments; balanced games; totally balanced games; local public goods, core convergence; equal treatment property; equal treatment core; approximate core; strong epsilon core; weak epsilon core; cooperative game; asymptotic negligibility

Bargaining and matching in small markets.

The present paper focuses on markets where trade is carried out through matching and bargaining and where at each date t = 0,1, ... a finite and exogenously given number of agents enters. Such markets are "small" in the sense that whether a match ends with trade influences matching probabilities at subsequent dates. For a small market we show that as the market becomes large, the equilibrium of the small market converges to the equilibrium of a limit market with a continuum of agents. Nonetheless, for any small market there exists a matching process such that the equilibrium of the small market significantly differs from the equilibrium of the associated large market with a continuum of agents, although equilibrium-path matching probabilities are the same in both markets. Therefore, matching models with a continuum of agents are not always a good approximation of small markets.Matching; Bargaining; Market equilibrium;

Prices, delay, and the dynamics of trade

We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading partner is costly, prices are determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero, even though the trading patterns continue to be inefficient and delay persists.Publicad