Posted on Categories:Game theory , 博弈论, 经济代写

# 经济代写|博弈论代考Game theory代写|JOINT DECISIONS

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## 经济代写|博弈论代考Game theory代写|JOINT DECISIONS

A simple way of inserting a “summary” negotiation component into a noncooperative game is to include joint-decision nodes in the game tree. ${ }^1 \mathrm{~A}$ jointdecision node is an abbreviated description of negotiation between players over some tangible objects, such as profit-sharing rules, monetary transfers, or whether to form a partnership. Thus, a joint-decision node represents a place in the game where players negotiate and establish a contract. We specify a joint decision when we do not want to create a full noncooperative model of the negotiation process and when we have a simple theory of how negotiation is resolved (by using, for example, the standard bargaining solution).

To represent joint decisions in a tree, we can employ the same devices currently used to specify individual decisions. We simply allow some decision nodes to be designated as joint-decision nodes. The joint-decision nodes are graphically represented by double circles to differentiate them from individual decision nodes. Furthermore, we label a joint-decision node with the set of players who are called on to make the joint decision. Branches represent the alternatives available to the players, as is the case with individual decision nodes. In addition, wherever there is a joint-decision node, we must designate one of the branches as the default decision, which is assumed to go into effect in the event that the players do not reach an agreement. ${ }^2$

A game with joint decisions is illustrated in Figure 20.1, which is a simple model of contracting between a supplier firm and a buyer firm. First, the firms jointly determine whether to contract and, if so, what damages $c$ to specify if the supplier (player 2) is caught providing a low-quality intermediate good. If they choose not to contract (which is the default decision), then the game ends and each receives nothing. If they contract, and firm 2 then provides a high-quality good, payoffs are 10 for the buyer and 5 for the supplier. By providing a lowquality good, firm 2 saves money. However, the low-quality good is useless to the buyer. (These ideas are captured by the numbers -6 and 10 .) But with probability $1 / 2$, the supplier is caught and damages are awarded by a court. (This is a payment of $c$ from the supplier to the buyer.)

## 经济代写|博弈论代考Game theory代写|NEGOTIATION EQUILIBRIUM

To analyze general games with joint decisions, we combine backward induction (more specifically, subgame perfection) with the standard bargaining solution; the former pins down behavior at individual decision nodes, whereas the latter identifies behavior at joint-decision nodes.

Given an extensive-form game with joint decisions, a specification of behavior at every information set is called a regime. This is simply a generalization of the “strategy” concept to include joint decisions. I use the following equilibrium definition:

A regime is called a negotiation equilibrium if its description of behavior at individual decision nodes is consistent with sequential rationality and its specification of joint decisions is consistent with the standard bargaining solution, for given bargaining weights.

This definition is not precise enough to be clear-cut in every game with joint decisions. In particular, we can run into two problems when trying to construct a negotiation equilibrium. First, we have to decide what is meant by “sequential rationality.” For example, we could use backward induction or subgame perfection. Second, how to apply the standard bargaining solution in some contexts may not be obvious, in particular where there is not transferable utility. I avoid these problems by focusing on games in which backward induction or subgame perfection can be easily employed (this is a wide class, by the way) and by assuming that players can transfer money whenever they negotiate. You can leave to interested hot-shot theorists the task of navigating the labyrinthine esoterica of more general application.

# 博弈论代写

## 经济代写|博弈论代考Game theory代写|NEGOTIATION EQUILIBRIUM

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