[2]An economy which is not in the image of is, by definition a regular economy.
[3]An atom of a measure space is a non-null set in the space which includes no non-null subset of smaller measure.
[4]Varian (1987)
[5]Si*is the optimal strategy of individual i in his/her strategy space.
[6]The New Palgrave: Game Theory (1989)
[7]Aumann (1989)
[8]Kreps (1989)
[9]Sargent (1992)
[10]Despite the inadequacies of the static Edgeworth-type framework, there have been some attempts to solve the determinacy problem using the static model. See Foldes (1964)
[11]Zeuthen (1930) was the first to realise the need for a strong (determinate) theory of bargaining. Then came the seminal work on game theory by von Neumann and Morgenstein (1944)
12See Sutton (1986) for an analysis and proof of the Rubinstein result.
[13]It can be shown that the first mover advantage can be removed from the model by allowing the time between rounds of offers to go to zero in the limit. However, the eventual outcome will still depend on the relative discount factors.
[14]Rather than discount factors you can introduce fixed costs for discontinued bargaining.
[15]For a fine critique of all things game-theoretic, see Kreps (1990b)
[16]See Binmore and Dasgupta (1987)
[17]The issue of time in games is of tremendous significance. The passage of time is costly because of the discounting of payoffs. Rubinstein's model bypasses this by identifying the most efficient offer in the first found.
[18]The issue of commitment concerns implicit and explicit contracting. The efficiency of explicit contracts depends on the ability of the legal system to enforce them. There is the problem of incomplete contracts from bounded rationality. See Milgrom and Roberts (1990).
[19]"Ignorance may not be as successful a leveller as death, but it has its uses in this direction", Binmore and Dasgupta (1987) lt is an unreasonable assumption in game theory that a player knows perfectly his own preferences and those of his opponent(s). It is quite often the case that relevent information is secret from one another. This is the concept of imperfect information. There also exists the problem of incomplete information. Agents can only play the game that they think they are playing. This game they play to the best of their (Bayesian) ability. The problem is that one player or both does not know which game they are in. Possession of this knowledge lends bargaining power and hence a higher share of the outcome. This fact can be used to explain delays in bargaining, and why we never see immediate outcomes, as Rubinstein claims to prove. [Rubinstein's model claims perfect knowledge of opponents preferences.]
[20]Theoretically, if you allow the time between offers to go to zero the duration of optimal conflict goes to zero. See Gul and Sonnenschain (1985).
[21]This principle allows the construction of incentive-compatible mechanisms that outlaw self-interested manipulative behaviour. See Wilson (1987).
[22] A form of opportunism (moral hazard) associated with suboptimal contracts. It is the problem of post-contractual hold-up due to bounded rationality in contract design. See Milgrom and Roberts (1990).
[23]Every game cited here can be taken to be static unless otherwise labelled. All payoffs accrue to (row, column) respectively. We assume familiarity with both the rules and the (matrix and extensive) forms of noncooperative games. For the stories behind the games the reader is referred to Rasmusen (1989).
[24]A powerful concept is one with a good ability to produce equilibria. A strong concept, on the other hand, is one which produces solid or robust equilibria.