Abstract
In the earlier chapters of this book I have presented the basic elements of the collective goal theory of cooperation (g-cooperation) and sketched another view of cooperation in terms of private goals (i-cooperation, analyzed by means of (CO)). The rest of the book will discuss g-cooperation and i-cooperation basically in a strategic (as opposed to parametric) context. Conceptual and mathematical tools related to game theory will be used below.
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Notes
Moulin (1995, p. 112) gives an example of the equivalence in question from the so-called marriage market. This is an exchange economy in which a) each man and each woman is assumed to own a personalized indivisible good (himself or herself), b) each man (respectively woman) wants and can consume at most one of the goods initially held by women (respectively by men) and derives no utility from the goods held by men (respectively women). There is no medium such as money. Here the core and the competitive equilibrium match. Here the only core is given by the set ((m1,w4), (m2,w3), (m3,w2), (m4,w1)). This core matching can be interpreted as a competitive equilibrium by choosing the prices as follows: p(m3) = p(w2) < p(m4) = p(w1) < p(m2) = p(w3) < p(m1) = p(w4).
Zlotkin and Rosenschein (1994) present a theory of cooperation for rational robots. They analyze cooperation game-theoretically in terms of deals (corresponding to the agreements of game theory) or, equivalently, joint plans, arriving at a characterization concerning the circumstances under which a deal can be taken to be a rational cooperative deal. A deal for Zlotkin and Rosenschein consists of sets of tasks (“part-actions”), one for each participant. In a deal each participant commits himself to carrying out his tasks (his part of the joint action). A key notion for them is that of a negotiation set (NS). NS is defined to be the set of all deals that are both individually rational and Pareto optimal. A deal d is defined to be individually rational if, for all i, the utility of d, viz., Utility(i,d), is nonnegative, and it is Pareto optimal if and only if there does not exist another deal which is better for at least one of the agents and not worse for the other. Utility(i,d) is defined to be the minimal cost of achieving the goal G(i) alone (without the other agent doing “anything”) minus the individual’s (expected) cost of carrying out his part of the deal d. The deal-making approach distinguishes between cooperative situations and compromise situations (Zlotkin and Rosenschein, 1994, p. 105). A cooperative situation is one in which there is a deal in the negotiation set which is preferred by both agents over acting alone. Indeed, in a cooperative situation cooperation is (physically and/or socially) necessary for utility maximization. In contrast, a compromise situation is one where there are individually rational deals for both agents. But both agents would prefer to act alone. The problem here is that acting alone is not (physically and/or socially) possible. Each agent must cope with the presence of the other agent in that situation. All of the deals in NS are better than leaving the world at its initial state. A conflict situation is one in which the negotiation set is empty. (However, I will not here discuss the technical details, such as the “worth of a goal” account of utilities.) In view of what has been said the following thesis is true if Zlotkin’s and Rosenschein’s notions of cooperation and compromise are used: (COOP) A deal for performing a joint action of type X is cooperative or is a compromise if and only if NS is nonempty (viz., the deal satisfies the conditions of individual rationality (rewardingness) and Pareto optimality). My approach gives a somewhat different analysis. First, we note that in the deal-making approach cooperativity is attributed to deals and not to joint actions, as in my approach, although it is easy to go back and forth between these two terminologies. My notion of a plan (or extensionally equivalently, an agreement) corresponds to the notion of deal in the first-mentioned approach. Secondly, my notion of cooperation in the broad sense of (CAT) of Chapter 3 covers both cooperative situations and compromise situations. Thus within my approach it is true that if NS is nonempty then we are dealing with cooperative joint action in the sense of (CAT). My notion of cooperative joint action is concerned with cooperative situations and compromise situations in the sense of the deal-making theory. (It also concerns norm-governed situations, but I will here ignore them.) Then, leaving out the requirement of the Pareto-optimality of deals, cooperative situations and compromise situations (in the sense of the deal making theory) exhaust cooperative situations in the sense of (CAT). What is left outside the cooperation and compromise in the deal-making approach? Cases in which NS is empty are such, and they are called cases of conflict in the deal making theory. However, if some persons do not find it rational to make a deal in a situation, that does not have to mean conflict the ordinary sense of ‘conflict’. Furthermore, cases of compromise in the sense of the deal making theory also involve genuine conflict (means-conflict). In the deal-making theory cooperation occurs only when cooperation is necessary in the situation in question. However, agents can surely cooperate even when cooperation is not necessary for their prudentially reaching their goals. Furthermore, the deal-making approach does not at all take into account the central notion of preference correlation. It can also be noted against the deal-making theory that it forgets not only the underlying preferences but also the underlying motivation (willingness, cooperative attitude) and concentrates on what kind of commitment is prudentially feasible. In this sense this approach is one-sided — at least if regarded as acceptable for ordinary human agents.
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Tuomela, R. (2000). Cooperation and Cooperative Game Theory. In: Cooperation. Philosophical Studies Series, vol 82. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9594-0_7
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