Academic journal article Economic Inquiry

Incomplete Contracting: A Laboratory Experimental Analysis

Academic journal article Economic Inquiry

Incomplete Contracting: A Laboratory Experimental Analysis

Article excerpt

I. INTRODUCTION

Williamson [1975] and Klein, Crawford, and Alchian [1978], among others, pioneered the notion that long-term contracts arise as a means of governing and protecting valuable investments in long-term trading relationships. Contract incompleteness results when some terms are left unspecified and usually is a result of practical difficulties in specifying contingent responses to unforeseen future states of the world. Macaulay [1963] finds that incomplete contracts are common in business dealings, and Holmstrom and Hart [1985] argue that "incompleteness is probably at least as important empirically as asymmetric information as an explanation for departures from 'ideal' Arrow-Debreu contingent contracts." A substantial formal literature has built on this pioneering research and includes work by Grossman and Hart [1986], Tirole [1986], Crawford [1988], Hart and Moore [1988], Fudenberg, Holmstrom, and Milgrom [1987], Milgrom and Roberts [1991], and Hart and Holmstrom [1987]. This formal literature has distilled the earlier notions down to a standard two-period model that is used as a foundation to much of contemporary research on contracting and the firm.(1)

To motivate this model, consider a single buyer and seller of some intermediate good, such as computer software. They anticipate innovative change in the design of the intermediate good, but cannot foresee the precise nature of the innovation. As a result the contract cannot be made contingent on the change in design. The benefit of the design change to the buyer is uncertain, but the buyer can make a transaction-specific investment in flexibility that increases the likelihood that the benefit will be large. Similarly the cost of implementing the design change is uncertain, but the seller can make a transaction-specific investment that increases the likelihood that it will be small. In the second stage the innovation is realized. The buyer and seller then enter negotiations, the outcome of which determines whether the innovation will be implemented and how the surplus added by the innovation will be divided.

This two-stage model is solved using the technique of backward induction. First a game theoretic solution is imposed on second-stage negotiations, and this solution determines how joint surplus is shared. This division of joint surplus is assumed to be foreseen in the first stage and is incorporated into each party's expected profit function. Equilibrium is then found when each (risk neutral) party chooses their own expected profit maximizing level of transaction-specific investment. One potentially testable implication of this model is that the future division of joint surplus directly affects the level of transaction-specific investment, but the level of transaction-specific investment does not affect the division of joint surplus.

The bargaining literature has progressed rapidly in the development of non-cooperative bargaining models with unique equilibria that are testable using laboratory procedures. Influential non-cooperative bargaining models include those of Rubinstein [1982], Binmore [1985], and Binmore, Rubinstein, and Wolinsky [1986]. Accumulated evidence from laboratory experiments on bargaining such as in Guth, Schmittberger, and Schwarz [1982], Guth and Tietz [1990], Ochs and Roth [1989], and Neelin, Sonnenshein, and Spiegel [1988], suggests that non-strategic factors may have a substantial effect on bargaining outcomes. Much of the experimental work has been with ultimatum games, where one player submits a share proposal to another, who can either accept or force breakdown. When breakdown results in zero payoffs, the (subgame-perfect) equilibrium proposal grants very nearly 100 percent for the person making the proposal and the residual to the person accepting the proposal. Laboratory experimental studies of these games are usually able to reject this hypothesis. These studies typically find that allocations tend to fall somewhere between equal splits and the hypothesized equilibrium allocation. …

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