Indenture as a self-enforced contract device: an experimental test.

• Author: Kritikos, Alexander S.

1. Introduction

   How can a principal (an agent) ensure that an agent (principal) will work (pay) if payment (work) precedes work (payment)? An effective contract binds the contracted parties to honor the agreed terms of trade. Besides preventing moral hazard, its administration cost should ideally be as low as possible. The diversity of contracts can be classified under (i) contracts enforced by costly third party administration (for example, the law) and (ii) contracts that are self-enforced by the contracting parties. While contracts with third party enforcement might suffer from prohibitive enforcement costs, self-enforced contracts can govern self-interested individuals with conflicting interests to complete successful economic transactions. (1)

   Recent empirical research finds, however, that complete contracts driven by extrinsic incentives, that is, monetary payoffs, to induce cooperation have their own limitations. These kinds of contracts potentially diminish the intrinsic motivation to cooperate voluntarily (Frey 1997; Benabou and Tirole 2003). (2) Therefore, contracts of a polar opposite nature of complete contracts were considered. Explicit contracts based purely on intrinsic motivation, such as trust and reciprocity, have proved to be reliable and may even outperform complete contracts in certain contexts (e.g., Fehr, Kirchsteiger, and Riedl 1993; Fehr, Gachter, and Kirchsteiger 1997; Guth et al. 1998; Falk and Kosfeld 2006). However, these positive results might not always hold. (3) For instance, trust and reciprocity can induce considerable levels of cooperation in trust games even when theory predicts defection (for example, Berg, Dickhaut, and McCabe 1995; Bolle 1998; Dufwenberg and Gneezy 2000; and Charness 2004), but the stability of such contracts is suspect over time. Convergence to noncooperation may occur if the game is played repeatedly (Zauner 1999).

   In this context, the present article experimentally tests for the first time the efficacy and the performance of the indenture game (IG) proposed by Kritikos and Bolle (1998), which is a self-enforced contract, incentive compatible in one-shot interactions where reputation plays no role. The IG attempts to combine the low costs of self-enforcement, reliability of incentive compatibility, and intrinsic motivations of trust and reciprocity. In the IG, the principal transfers the first half of an indentured (torn) banknote to the agent. The agent then decides whether to exert effort. The principal can complete the transaction by sending the other half of the indentured banknote to the agent. Kritikos and Bolle theoretically show that cooperation is a mutual best reply for principal and agent. Among the multiple equilibria, forward induction (van Damme 1989) selects cooperation as the unique stable equilibrium--cooperation is thus self-enforced.

   The central feature of this contract is this: A principal sends a signal of his intention to cooperate, that is, to complete the transaction with a remittance of the second half of the indentured note, thereby paying in full, by sending the agent the first half of the indentured note. Following the reasoning of Berg, Dickhaut, and McCabe's (1995) trust game, it is also an investment of trust in the agent. Agents will interpret this action as a signal of intention to cooperate, by forward induction logic, and thus will accept the contract; in effect, they naturally self-select themselves into performing the task. As with the trust game, the fulfillment of tasks is positive reciprocity to the principal if the first half of the indenture is perceived as trust invested in the agent. In the final stage of the game, although the principal is indifferent between transferring and retaining the second half of the indentured note, it is consistent with the signal sent in the first stage (that is, the transfer of the first half) that the second half be sent. By doing so the principal can reciprocate (reward) the agent's trustworthiness without having to sacrifice any additional material payoff, in contrast to the trust game. In other words, "cooperative" principals are naturally self-selected into eventual compliance with the contract. Thus, selfish players have a pecuniary incentive, while reciprocal players have an intrinsic motivation to cooperate.

   The method of indenture can be applied to real-world situations. For instance, employers invest in a management trainee with training (the first half of indentured note), and a positive or negative reference letter (transferring or keeping the completing half of indentured note), in exchange for a minimum term of work after the training phase. (4) A second example is the buying of a car by making use of a bank loan. To collateralize the loan, banks usually keep the car registration documents, without which the car cannot be sold. These documents (the second part of the banknote) are handed out by the bank only if the owner of the car has repaid the loan (the effort) in full. (5)

   It is important to test the efficacy of indenture as a self-enforced contract device, to test its robustness across parameter variations, and to understand the method and its limitations-when theory and empirical evidence do not (fully) coincide. In practical terms, laboratory experimentation allows us to test such a mechanism design ex ante at low costs, relative to the ex post costs involved in natural experiments. (6) Based on laboratory experiments, our paper compares cooperation rates in the IG with that in a three-stage centipede game (CG) with similar parameter values (for example, gains from trade). Theory predicts no cooperation in the CG. We interpret the cooperation observed in the CG as a benchmark for the "natural rate of cooperation," defined as the rate of cooperation observed in a game where individuals have the (pecuniary) incentive to unilaterally deviate (not cooperate).

   The rest of the article is organized as follows: Section 2 presents a further analysis of the IG and CG; section 3 describes the experimental design; section 4 reports our results; and section 5 discusses and concludes.

2. Theoretical Background

   The IG is a three-stage game, following Kritikos and Bolle (1998): Two parties can potentially enter into trade, exchanging a service (by the agent) for a payment (by the principal). Principals and agents make nonbinding agreements. (7) Players cannot be forced to comply with the "agreement" (the word "agreement" is a misnomer if only one party wishes to engage in trade). In stage 1, a principal can initiate a contract by indenturing a banknote of value e by tearing it in two. A principal chooses whether to cooperate by sending one part of the indentured banknote (the first half) to the agent (call this action [c.sub.1]) or to take the outside option and keep the entire banknote (call this action [n.sub.1]).

   Tearing the banknote in two renders both pieces worthless when separated. The banknote regains its value only when the principal sends the agent the matching and completing half (the second half). In stage 2, the agent may provide ([c.sub.2]) or refuse to provide the service ([n.sub.2]). Upon refusal, there is no "contract," and the agent keeps b, the outside option, which is the cost he has to incur in providing the service, where b e. Here he then has the choice between transferring ([C.sub.3]) or withholding ([n.sub.3]) the second part of the indentured banknote. (8) Thus, in the IG, in stage 1, the principal virtually "gives up his entire stake" (although only the first half is transferred, it no longer holds pecuniary value for the principal) to the agent (albeit the intermediate payment in hand holds no pecuniary value for the agent). In the final stage, the principal is indifferent between transferring and withholding the completing half. Figure la describes the IG.

   [FIGURE 1 OMITTED]

   Let us consider the principal's strategies. The principal can, in stage 1, choose between two actions--initiating a contract or not initiating it. In stage 3, the final stage, the principal has the choice between two further actions--transferring or retaining the second part of the banknote. Given that the agent also has to choose between two actions in stage 2--to provide or refuse to provide the service--the principal has the following set of four strategies at hand if he enters the subgame of indenture by sending the first half of an indentured banknote: (i) always transfer the second half regardless of the agent's choice, (ii) never transfer the second half regardless of the agent's choice, (iii) transfer the second half only if the agent has not provided the service, or (iv) transfer the second half only if the agent has provided the service. (9)

   Backward induction identifies four subgame-perfect equilibria. If the principal chooses strategy (iv), it is a mutual best reply for both to take cooperative actions throughout the game, leading to outcome ([c.sub.1], [c.sub.2], [c.sub.3]). If the principal chooses any of the other three strategies, the best reply of the agent is to defect, and the principal is better off not initiating the contract, leading to outcomes ([c.sub.1], [n.sub.2], [c.sub.3]), [c.sub.1], [n.sub.2], [n.sub.3]), and ([n.sub.1], [n.sub.2], [n.sub.3]). Thus, players have conflicting interests in this game.

   Among the multiple equilibria, the equilibrium selection concept of forward induction (van Damme 1989) selects ([c.sub.1], [c.sub.2], [c.sub.3]) as the unique stable equilibrium. The logic of forward induction requires the following weak property to be satisfied: "[...] in generic 2-person games in which player i chooses between an outside option or to play a game F of which a unique (viable) equilibrium [[psi].sup.*] yields the player more than the outside option, only the outcome in which i chooses F and [[psi].sup.*] is played in F is plausible" (van Damme 1989 p. 485). (We replace "[e.sup.*]" in van Damme's original text with...