Resumen de Conflict as a part of the Bargaining Process: Theory and Evidence
Santiago Sánchez Pagés 
Since Nash�s seminal contribution, the bargaining problem has been traditionally summarized by the set of feasible utility possibilities and a threat point.
The latter is meant to be the outcome in case of disagreement, a ground floor payoff they receive in the hypothetical non-cooperative game that would follow.
Its influence stops here: How the surplus of cooperation is finally shared is totally independent of the forces that determine the location of the threat point. In the last years, several authors have tried to reformulate this approach by giving more structure to agreements by incorporating information about how disagreement is actually solved. This is the central issue in Bester and Warneryd (1998), Esteban and Sakovics (2000), Fearon (1996), Grossman (1994), Horowitz (1993) and Powell (1996). These models obtain agreements in the shadow of conflict (war, redistribution by force...) that are influenced by the relative power of the parties. With the exception of Esteban and Sakovics (2000), all these papers depict conflict as a costly lottery: Either one party or the other wins and captures the surplus. Thus, invoking conflict is a gameending move, an alternative to the bargaining process.
On the contrary, casual observation shows that the main reason behind the end of conflicts is not the total collapse of one of the parties but agreement on stopping hostilities: India and Pakistan do not use nuclear weapons, they only engage in skirmishes; Pepsi and Coca-cola do not engage in worldwide price wars, but only national; family arguments do not necessarily imply divorce...
That is, conflict is not mainly a �fight to the finish� but a part of the bargaining process.
To illustrate this point consider the following example: Suppose that two agents have incomplete information on the strength of their opponent in case of conflict, and that both parties are strong but believe that they are facing a weak opponent. Then, the perceived threat-point will be out of the bargaining set and the result of the negotiation, following the papers above, would be a conflict fought to the finish. However, notice that if parties can engage in a conflict of limited scope that does not entail the end of the game, it may convey information about relative strengths and create a range of possible agreements.
Hence, in this paper, following the pioneering work of Clausewitz (1832) and more recently Wagner (2000), we propose a taxonomy of conflicts (wars, strikes or revolutions) into REAL and ABSOLUTE conflicts and explore the consequences of incorporating them in a bargaining model with one-sided offers and one-sided incomplete information. In economically familiar terms, absolute conflicts have an ex-post interpretation: they are fought when one party losses completely the hope of reaching an agreement through ordinary methods. So it tries to make the opponent defenseless in order to impose its most preferred outcome without opposition. On the other side, real conflicts (that receive this name because, as argued in Wagner (2000), few strikes or wars we should observe if their consequences were always the defeat of one of the parties) have and ex-ante interpretation: they are fought before normal bargaining because they can help to improve the position in negotiation by revealing information about the true relative power of the parties. Therefore, it is the possibility of ending the conflict in a settlement what differentiates them.
From a formal point of view, revelation of information through conflict introduces a novelty in the models of bargaining with incomplete information:
In these models, parties have incentives to misrepresent information. This fact usually leads to very complex models and multiple equilibria. However, the result of a conflict is not subject to manipulation because its outcome depends on the true relative strengths of the parties. The only strategic variable is the decision of invoking it or not, and bluffing the other party becomes a very difficult task. Following Wagner, conflict �is an experiment that allows parties to test competing hypothesis about the outcome of an absolute conflict�.
Our paper has two parts: In the first part we develop a bargaining model that takes into account the issues discussed above. In the second, we test the implications of the model with real data on wars and strikes. In the model we propose two impatient and risk-neutral players have to decide how to share a cake one dollar worth. One of the parties knows the true realization of the relative strength and therefore the outcome of the absolute conflict. Each period, this party makes an offer to the other, who can accept or reject. Agreement makes the game end but disagreement triggers a �battle�. Although it is won by one of the parties, this real conflict does not entail the end of the game.
However, it has two other effects: possible agreement is delayed one period and it conveys information because the outcome of the battle is related to the realization of the relative strengths. Then, each battle makes the uniformed party to learn about the true disagreement payoffs in case of conflict. We obtain the following results: Agreement may be immediate if the loss of the cake due to absolute conflict is sufficiently high and players are impatient enough. Then, players may prefer to settle as soon as possible in order to avoid such unfavorable outcome. On the other side, we also show that the creation of surplus is a necessary and sufficient condition for agreement. That is, once agreement is possible, the informed party has no incentives to take the chance of improving its position. Therefore, the number of battles (or the duration of the real conflict) depends decisively on the gap between the perceived and the real disagreement payoffs, because if the uniformed party is excessively optimistic it may take several periods to bring the disagreement point inside the bargaining set.
This result has a clear implication regarding real-life conflicts: Given that they are a way of learning for the parties, they are more likely to end the more they last. Then, we pursue a hazard rate approach using duration data.
The hazard rate is the conditional probability that an event that has lasted t period ended at period t + 1. Our theory would predict that this hazard rate must be increasing in time. We test this hypothesis first with data on Extrasystemic wars from 1816 to 1991. This wars are fought between a state and a non-state entity. They include mainly imperialistic and colonial wars. They are appropriated for our study because they are clear asymmetric situations (moreover, these conflicts have not been analyzed in this fashion so far). We obtain clear evidences that these type of conflicts show increasing hazard rates supporting our theory. In the second case we deal with U.S. data on strikes and holdouts. A holdout is an impasse; a period of time after the collective contract has expired where workers keep working at the same conditions. They have been pointed out as informational devices by Gu and Kuhn (1998) and we postulate that they are real conflicts whereas strikes can be think as absolute conflict. Consistently with our hypothesis, strikes are more likely to occur if a holdout has not occurred previously and, if it did, they last more the shorter the holdout. This gives support to our analysis and suggest that we observe conflict in real world because sometimes they are necessary for obtaining an agreement. To understand why conflicts occur may be helpful to avoid them
