Bargaining and Coalition Formation Dr James Tremewan - PowerPoint PPT Presentation

Bargaining and Coalition Formation Dr James Tremewan (james.tremewan@univie.ac.at) Experiments on Cooperative Solution Concepts

Experiments on Cooperative Solution Concepts Experiments on Cooperative Solution Concepts • ”A test of the core, bargaining set, kernel and Shapley models in N-Person Quota Games with one weak player,” Horowitz (1977). • Experiments on four and five-player versions of the ”Three Player Game” we looked at last week. • ”An Experiment on a Core Controversy,” Yan and Friedman (2010). • Experiments on the ”Glove Market” from last week, and a five player version. • ”Committee decisions under Majority Rule: An Experimental Study,” Fiorina and Plott (1978). • Classic paper testing a variety of theories in ”spatial games.” • ”Patterns of Distribution in Spatial Games,” Eavey (1991). • Challenges some of the conclusions of the previous paper. 2/28

Horowitz (1977) Horowitz (1977) • Experiments on ”n-person (n-1) quota games” with one weak player for n ∈ { 4 , 5 } . • n-player game where the value of a coalition is positive if and only if it contains at least n-1 players. • Values of coalitions are chosen such that in core allocations: • One player (the weak player) will receive zero. • A different range of payoffs is predicted for the other players. • The value of the grand coalition is equal to the highest value of (n-1) coalitions. • Example for n = 3 from last week: • v ( { 1 , 2 , 3 } ) = 10, • v ( { 1 , 2 } ) = 10, v ( { 1 , 3 } ) = 3, v ( { 2 , 3 } ) = 2, • v ( { 1 } ) = v ( { 2 } ) = v ( { 3 } ) = 0. 3/28

Horowitz (1977) 3-Player Quota Game With One Weak Player (0,10,0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3,7,0) . . . . . . . . . . . . . . . . . . . . ✉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shapley value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ✉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8,2,0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ✉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10,0,0) (0,0,10) 4/28

Horowitz (1977) Horowitz (1977): Implementation • Mediated through computers. • Comunication occured in fixed order, and restricted to six keywords: offer, accept, reject, ratify, pass, solo. 1 • If an offer was accepted by enough people, there would be a ratification stage where a preliminary agreement becomes binding. • Results: as predicted by the core, the weak player always received zero! 1 ”Solo” meant withdraw from game which is pointless in these games... the program ( coalitions : see Kahan and Rapaport, 1974) was designed for general games in characteristic form. 5/28

Horowitz (1977) Horowitz (1977): Results (4 Players) 6/28

Horowitz (1977) Horowitz (1977): Results (5 Players) 7/28

Horowitz (1977) Horowitz (1977): Results • The core does a good job of predicting outcomes: • The weak player always gets zero. • For 8/9 types of players, the average payoff was in the core. • 90/108 individual payoffs were within the core. • Where payoffs fell outside of the core they were in the direction of the Shapley value. 8/28

Yan and Friedman (2010) Yan and Friedman (2010) • Market Game: • s sellers with cost c and b buyers with valuation v , where v = c + 1. • Each seller has precisely one good, and each buyer can buy one. • For s = 1 and b = 2 this game is equivalent to the Glove Market game we looked at last week. • If s > b the sellers are on the ”long side” of the market and buyers on the ”short side” (and vice versa). • In general, the core predicts that the players on the short side will extract all the surplus. • This results in the extreme prediction that switching one buyer to a seller can switch the entire surplus from one side to the other, often seen as a bad feature of the core: intuitively players on the long side should be able to collude in some way. • This paper tests this prediction for s = 1 and b = 2, and s = 2 and b = 3. 9/28

Yan and Friedman (2010) Yan and Friedman (2010): Implementation • Uses continuous double auction (CDA): Buyers and seller post bids and offers publicly, which can be accepted in real time. • Three treatments: • Std: no communication (apart from bids and offers). • Chat: free pre-play (public) communication in online chatroom. • Barg: allows chat, and for players on the long side to form collusive agreements. • A collusive agreement means one or more players withdraw from trading and give another the right to buy or sell their good in exchange for a proportion of the profit. These agreements can be withdrawn from unilaterally, but only before a trade has been implemented. • Designed to give collusion its best shot. • After 8 periods, a “long-side” subject switches roles. • In following slides, SSS (Short Sider Surplus Shares) = the fraction of the surplus obtained by the short sider. 10/28

Yan and Friedman (2010) Yan and Friedman (2010): Results 11/28

Yan and Friedman (2010) Yan and Friedman (2010): Results 12/28

Yan and Friedman (2010) Yan and Friedman (2010): Results 13/28