Journal of Economic Behavior & Organization Vol. 42 (2000) 137–139
Indenture: a viable contract for a sequential one-shot
Prisoners’ Dilemma
A reply to Holt
Alexander S. Kritikos
∗, Friedel Bolle
Lehrstuhl für Volkswirtschaftstheorie, insb. Mikroökonomie, Europa-Universität Viandrina, Frankfurt (Oder), Germany
Received 9 November 1998; received in revised form 27 May 1999; accepted 27 May 1999
Abstract
Holt’s argument is wrong. A closer look at the structure of the game and at the equilibrium selection criterion shows that mutual co-operation is secured in an Indenture Game. ©2000 Elsevier Science B.V. All rights reserved.
JEL classification: C72; D89
Keywords: Game theory; Prisoner’s Dilemma; Trust; Indenture
In Kritikos and Bolle (1998) we propose a mechanism to induce co-operation between a principal and an agent if service and payment are not exchanged simultaneously and if none of both parties is sure whether the other party will fulfil its part of an unenforceable contract. The problem is solved by suitable transaction structure — symbolically described as indenturing a banknote. In this game structure co-operation is one possible Nash equi-librium — even in the absence of standard mechanisms to induce non-defection behaviour. Due to the principal’s indifference in the final node of the game there exist other equilibria leading to mutual defection. Forward Induction selects the co-operative outcome as the unique equilibrium.
Holt (2000) argues that the principal may simply resell the indenture to a new owner after the agent had performed the initial service. In that case the principal would indeed not be indifferent in the final node of the game which would cause mutual defection of rational players. This causes Holt to conclude that our finding is internally inconsistent. But Holt’s
∗Corresponding author. Tel.:+49-335-5534-248; fax:+49-335-5534-390. E-mail address: kritikos@euv-frankfurt-o.de (A.S. Kritikos).
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argument is wrong because a potential reselling of the indenture does not challenge this special transaction structure. By following his argument we can clarify the issue.
First, Holt confuses the consistency of an argument with the relevance of the transaction structure. If the transaction structure is robust, then the co-operative solution is viable. There are two reasons why the structure is robust:
1. Recall that it is the principal who selects the Indenture Game and who first bears the risk of loosing his stake when he makes the initial move towards the Indenture Game. Therefore, it is in his own material interest to shape the game properly so that a credible commitment is created as to the structure of the Indenture Game. The Principal has to
care for the indifference in the final move of the game by excluding any possibilities
of reselling or renegotiating the indenture so that it is the Principal’s perfect strategy to transfer the Indenture after the agent has served. In other words: the Principal’s response rule must be in place before the agent has to perform his service. (By this means the authors are saved of being trapped into the transparent fixed disposition fallacy, which is extensively discussed in Binmore (1994).) In our example the employer cannot resell the obligation of issuing a reference after an employee has quit the job. There is simply nothing to be resold. The employer can only provide the employee with a positive or a negative reference. Thus, the employer has structured the game properly.
2. Although we think that (1) is central, this argument might be countered by asserting that the problem of reselling the indenture is simply defined away. Let us, therefore, assume that the principal is not able to structure the game properly so that reselling the indenture is not completely excluded. Let us further assume that he aims to resell the indenture after the agent has performed the initial service and that all potential principals have access to the information that the agent has fulfilled his part of the indenture. Will there be any new principal who will pay a positive amount for an already served indenture? Clearly no — because an agent will never serve any second claim1. The crucial point is that — in contrast to Holt’s assertion — the agent does not ‘face the exact same game’. A new principal buying an already served indenture — is not able to signal how the rest of the game should be played. Forward Induction cannot be applied. Therefore, no principal would be able to resell the indenture2 and is still indifferent in the final step of the game. He has to decide whether he will fulfil his part of the contract. The agent will still stick to the agreement, if the probability of being matched with a complying principal is sufficiently large.
As is shown in Kritikos and Bolle (1998) for the case of a possible renegotiation, there are only two equilibria if reselling is always possible. One equilibrium implies not entering the exchange at all, the other ‘indenturing, not reselling’ for the principal and ‘fulfilling the service at the first stage but never after a reselling’ for the agent. The reason is the following: Recall that the principal and the agent act within a sequential game. An agent serving a second time has to expect further claims either by the same principal or by the next principal
1It is exactly here where Holt failed to think about the next step: reselling is not a big issue, because no rational person would buy an indenture which was served once.
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after the indenture was anewly resold. Therefore, equilibrium behaviour requires that he does not comply to any further claim irrespective whether this is posed by a new or the old principal.
Of course one could object that a new principal is able to make a perfect commitment which may convince the agent that he will definitely receive the indenture after having worked for the new principal. However, if the new principal is able to make a perfect commitment, the old should be able as well and we are back in (1) so that (2) does not pose any problem at all.
Proposition. (1) It is shown that the principal should try to exclude any additional claims
against the agent after he has served the initial indenture. (2) However, even if this is not possible no agent will ever serve any second claim so that the indenture remains to be a viable contract.
Therefore, if a sequential Prisoners Dilemma Game (the conventional transaction struc-ture) is converted into the transaction structure of the Indenture Game, Forward Induction makes co-operation the sole economic equilibrium — surprisingly indeed.
References
Binmore, K., 1994. Game theory and the social contract. In: Playing Fair, Vol. 1, MIT Press, Cambridge, MA. Holt, G., 2000. A comment on indentured servitude: in response to Kritikos and Bolle, Journal of Economic
Behavior and Organization, 42, in press.
