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Bargaining and boldness. (English) Zbl 1023.91003
Games Econ. Behav. 38, No. 1, 28-51 (2002); corrigendum ibid. 41, No. 1, 165-168 (2002).
The author studies a multiperson bargaining problem described in the form of the following Shaked’s game: There are \(n\geq 2\) bargainers (players). In each period \(t=1,2,\dots\) , player \(i=t\pmod n\) submits a nonnegative vector proposal \(x_t = (x_t^1,x_t^2,\dots , x_t^n)\) satisfying \(\sum_{j=1}^n x_t^j =1\). The other players \(j \neq i\), either accept or reject that proposal. If all of them accept \(x_t\), then the game concludes and each player \(k\) receives the share \(x_t^k\). In other case, two subcases can occur:
(1) with a constant probability \(1-\rho\) the game concludes with zero proposal \(x_t = (0,0,\dots , 0)\); (2) with probability \(\rho\) the play passes to the next period \(t+1\), and player \(j=t+1\pmod n\) becomes a new proposer, and so on (here \(\rho\) is fixed for all periods). The payoff of a player \(k=1,2,\cdots , n\) in the game is \(V^k(\rho^s,x_s^k)\), where \(V_k\) are continuous functions, and \(s\) is the period in which the proposal \(x_s\) has been accepted by all the players.
The game is studied in context of the existence and uniqueness of Stationary Subgame-Perfect Equilibria (SSPE), and their form is considered. Also the limit behavior of SSPE as \(\rho \rightarrow 1\), and their limit outcomes (called equally marginally bold) are analyzed. The paper ends with a comparison of such outcomes with Nash outcomes.

MSC:
91A20 Multistage and repeated games
91A10 Noncooperative games
91B52 Special types of economic equilibria
91A06 \(n\)-person games, \(n>2\)
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