CUMBRES Y ABISMOS

In the previous chapter, it was assumed that the government offers a pricing function that responds to the lobbying efforts of the private players. Each player, therefore, had an opportunity to obtain a favourable price by spending resources in lobbying the government. Players were assumed to maximize rental payoffs - their sectoral rental income net of lobbying expenditure. Nash behaviour was assumed on the part of each player while choosing their optimal lobbying expenditures. In other words, given the pricing function of the government, it was assumed that each player takes the lobbying expenditure of the other player as given, and chooses his own lobbying expenditure to maximize his rental payoff. It was shown that at least one

noncooperative Nash equilibrium exists in a lobbying economy of this type.

However, the assumptions of a noncooperative game also imply that players do not communicate and cooperate with each other in adopting joint strategies even if it may yield strictly higher payoffs to both the players. Recognizing the restrictiveness of this approach we are changing the rules of the game in this chapter. Here, we will allow players to communicate, negotiate and enter into a binding agreement if it is

individually rational to do so.

Each player is now free to choose between noncooperation and cooperation with the opponent. This possibility has expanded the strategy set of each player. Not

spending on lobbying the government and demanding a particular tariff rate with the opponent are new additions to the noncooperative strategy sets. Now, a player may choose to lobby the government, may unilaterally decide not to lobby the government, or may demand a binding agreement from the opponent on a particular tariff rate for not spending on lobbying the government for tariff changes.

These changes in the rules of the game transform the tariff game into a bargaining problem - where players bargain over the tariff rate (or domestic relative price). Player 1, the import competing sector, prefers a higher tariff rate and player 2, the exporting sector, prefers a lower tariff rate (prefers an export subsidy!). The main purpose of this chapter is to obtain the tariff rate that solves the bargaining problem in the tariff game.

We attain the objective in a sequence of steps. Nash's original solution to bargaining problems in which players hold unequal bargaining powers yields payoff

distributions that depend on the way players are ordered in the vector space. We show this well-known result, having specified the process of tariff determination as a standard fixed-threat Nash bargaining problem. We then provide a more precise definition of the bargaining power of a player, and argue that the distribution of bargaining power has to be included in the mathematical description of the game. We call it a generalized bargaining game, which is defined by the bargaining set, the disagreement payoffs, and the distribution of the bargaining powers of the players. We then show that the so-called asymmetric Nash solution to a bargaining problem is in fact symmetric. We provide this result as a corollary to Roth's theorem that characterizes the Nash solution to an

arbitrary bargaining game with asymmetric bargaining powers. Since the solution is symmetric, we have called it the generalized Nash solution rather than calling the ‘asymmetric Nash solution’.

We ask, then, why players reach an agreement in a bargaining game. Binmore, Rubinstein, and Wolinsky (1986) have argued that players reach agreement because (a) they have a high time-preference rate (so that they value current above future gain), this induces an agreement and/or (b) they fear a third party may intervene; the opportunity of gain would then be entirely lost and a disagreement would result This increases their temptation to conclude the deal. They have further shown that the difference in players' fear of disagreement, and the difference in players' time-preference rates can be

captured by the difference in the player's bargaining powers.

Aumann and Kurz (1977a) have employed the concept of ‘fear of ruin’ resulting from possible disagreement. At the Nash equilibrium, they show, players hold identical fear of ruin.

We have argued that Binmore, Rubinstein, and Wolinsky's ‘fear of

disagreement’ and that addressed by Aumann and Kurz are different, and that each one can provide a separate motivation for the players to reach agreement. We have further argued that Aumann and Kurz's concept of ‘fear of ruin’ can not be captured by differences in players' bargaining powers, because it is not a constant number. It changes during the bargaining process as the players attain different levels of gains. Since, Aumann, and Kurz's concept of ‘fear of ruin’ was defined for bargaining games with equal bargaining powers, we have attempted to generalize this concept for an arbitrary distribution of the bargaining power among the players so that all sources of the ‘fear of ruin’ could be addressed simultaneously.

We have proved that the equality of the generalized fear of ruin constitutes a separate characterization of the generalized Nash solution to an arbitrary Nash

bargaining problem, including the tariff game. This result is new, and more importantly, it holds the key to the results of our subsequent chapters. We have also shown that if the

fear functions are well-behaved, then the generalized Nash solution to the tariff game is stable.

Our result is different from that obtained by Svejnar (1986), who showed that the generalized Nash solution also implies equality of generalized fear of ruin, and that equality of generalized fear of ruin together with usual axioms implies the generalized Nash solution. We have shown that equality of generalized fear of ruin, when each player holds a strictly positive fear of ruin, yields the generalized Nash solution without any reference to the other axioms. The advantage of this result is that we can now obtain the generalized Nash bargaining solution in a different way - using players' fear of ruin and the distribution of bargaining power. This result seems to be useful in simple and intuitive demonstration of the bargaining process and the generalized Nash bargaining solution.

Finally, with a summary of the bargaining problem, we have stated the necessary and sufficient condition for the Nash solution to the bargaining problem of the tariff game. We have also attempted to identify the fear of ruin with the concept of endogenous bargaining power of the players.

This chapter is organised into five sections. The first section describes the setting of the game in the form of a standard bargaining problem. The second section describes the Nash solution to the bargaining problem. It is argued that the generalized Nash solution to a bargaining problem that allows unequal bargaining power is not asymmetric as is commonly believed. In the third section, the bargaining process is described in terms the concept of fear of ruin, where we argue that the fear of

disagreement referred to by Aumann and Kurz and the fear of disagreement referred by Binmore, Rubinstein and Wolinsky are different, and a generalization of the concept of fear of ruin has been proposed. In the fourth section, the main result that the equality of generalized fear of ruin constitutes a separate characterization of the generalized Nash bargaining solution, is proved. Finally, in the fifth section the basic contention of the chapter has been summarized.

The contribution this chapter makes to the thesis is that it examines the tariff game in a bargain-theoretic framework thoroughly. It obtains the necessary and sufficient condition that characterizes the generalized Nash solution to the bargaining problem in the tariff game. The next chapter will take up this condition and embed it into the policy-exogenous general equilibrium model (described in chapter 3) to obtain a tariff-endogenous general equilibrium model of the economy.

6.1 Rules of the Game and the Bargaining Problem

We continue to assume that the government is a support maximizer.1 So, if the two players - owners of the specific factors in the two sectors - agree on some issue, the best policy for the government is to implement the agreement. This will guarantee the maximum support to the government. If they disagree, then the game will be played as described in the previous chapter: the government will choose a policy that maximizes its political support subject to the reaction functions of the two coalitions (players). The government behaves as a Stackelberg leader vis-a-vis the private players - it announces its policy function. The two players behave as Nash players against each other taking the government's policy function as given.

Noncooperative equilibrium

disagreement payoffs

Payoffs in cooperation Figure 6.1

Thus, in the tariff game, the new rules of the game would mean the following to the players: If the two players agree on a particular tariff rate, then the government will announce and implement that rate. Otherwise, (if they fail to agree on any rate) the government's pricing function will be in effect and the two players will play a non cooperative game. The tariff rate that arises at the Nash equilibrium of the game will be implemented. Therefore, if the two parties cooperate with each other - that is, they agree on a tariff rate, and agree not to lobby the government, then they receive the resulting rental income as their payoffs. If they cannot cooperate, then they receive the

1 For analytical similarity between the choices of a support maximizing government and a welfare

resulting rents less the lobbying expenditures as their payoffs. This situation is illustrated in Figure 6.1.

For simplicity, in figure 6.1, identical Cobb-Douglas production technologies are assumed. The curve CD represents the rent transformation frontier (RTF) for given endowment of factors, and international prices (see chapter 4). Suppose that the parties could not agree on any tariff rate, and chose to play a noncooperative game. Suppose further that a unique noncooperative Nash equilibrium is obtained with lobbying expenditures and f}2 yielding a domestic price ratio ^ . Then the sectoral payoffs, which are rental incomes net of lobbying expenditures, are given by 1% and f l 2 for sector 1 and sector 2 respectively.

Recall that sectoral rental incomes are measured in units of own output Let the point E (in figure 6.1) denote the payoff combination and the point R denote the

combination of sectoral rental incomes at the noncooperative Nash equilibrium. Then E defines the disagreement payoffs - the payoff to each player if they can not reach an agreement.

However, if the two players cooperate, then they need not spend resources in competitive lobbying, and they can stay on the rent transformation frontier CD. For example, if the players had accepted the price Px and agreed not to participate in competitive lobbying, both would have received payoffs corresponding to the point R, which represents a combination of higher payoffs than that corresponding to the point E.

Thus, given that E would be the outcome of disagreement, the shaded area EFG represents the set of payoff combinations that the two players can improve upon by choosing cooperation rather than noncooperation. The arc FG represents the set of feasible and Pareto efficient payoffs. Any point on it is strictly better than point E, and any movement along it hurts one player or the other.

As indicated in the previous chapter, a noncooperative Nash equilibrium may not be unique. In the case where there are multiple equilibria it is not possible to identify the disagreement payoffs of the game with a particular noncooperative Nash equilibrium of the game. Since all the Nash equilibria are characterized by non-zero lobbying by all players (Lemma 5.4), the resulting equilibrium payoffs in each of the noncooperative Nash equilibria are not on the curve CD, but lie inside it. Therefore, the above argument is equally applicable irrespective of which of the noncooperative Nash equilibria is attained.

In general, all payoff combinations represented by points in the area OCD can be regarded as the set of feasible outcomes and that the set of noncooperative Nash

equilibria, which is a subset of feasible outcomes, can serve as potential disagreement payoffs. The sets of points in the areas like EFG are always non-empty and contain points that, in terms of payoffs, strictly dominate points like E. Therefore, there is always an incentive to the players to get involved in a bargaining process and search for a mutually agreeable tariff rate.

There are three reasons to believe that all agreements reached in a tariff game will be enforceable. First, playing a noncooperative Nash equilibrium strategy is always a credible threat that can be issued by any player against the other player, and that works as a deterrent against possible deviant behaviour of either player. Therefore, when the players agree not to spend on lobbying the government and agree on a tariff rate, they will most likely find it not rational to deviate from it. Second, as Subik (1982) argued, constitutional arrangements and the presence of government as the enforcing agency makes players almost incapable of deviating from the agreement. Moreover, if the government is a support maximizer, as we have assumed, then it will have an

incentive to implement such cooperative agreements. Third, the tariff game is a periodic game. It is played repeatedly. Cooperative outcomes of repeated games are, in general, self-enforcing (Fudenberg and Maskin, 1986; Friedman, 1986).