An experimental study of the holdout problem in a multilateral bargaining game.

AuthorCadigan, John
  1. Introduction

    When an economic exchange requires agreement by multiple independent parties, the potential exists for an individual to strategically delay agreement in an attempt to capture a greater share of the total surplus created by the exchange. This "holdout problem," as it has been called, is a common feature of the land-assembly literature (Coase 1960; Eckart 1985; O'Flaherty 1994; Strange 1995; Menezes and Pitchford 2004a, b; Miceli and Segerson 2007; Miceli and Sirmans 2007; Nosal 2007) because land development and urban renewal frequently require the assembly of multiple parcels of land. Similarly, the production of new products may require the use of multiple intermediate patented goods. Strategic delay and holdout have also been studied in other contexts, including debt restructuring that requires acceptance of an exchange offer by multiple creditors (Brown 1989; Datta and Iskandar-Datta 1995; Hege 2003; Miller and Thomas 2006) and wage negotiations (Cramton and Tracy 1992; Gu and Kuhn 1998; van Ours 1999; Houba and Bolt 2000). In each case, it may be difficult or impossible to distinguish strategic holdout behavior from more genuine disagreement arising because a buyer's offer is below a seller's reservation price.

    Because of the potentially large inefficiencies arising from failed exchanges in land assembly, the holdout problem has been cited as one justification for eminent domain, the legal power of the state to expropriate private property without the owner's consent. (1) Eminent domain has traditionally been used in the United States to acquire land for public projects but has been increasingly used to facilitate, with considerable controversy, the transfer of property from one private owner to another. (2) In most cases, eminent domain is accompanied by a requirement that just compensation be paid, generally interpreted to be fair market value. (3)

    From an economic perspective, whether the application of eminent domain can be viewed as efficient depends on the relative values attached to the parcels by the parties involved in the exchange and the costs associated with delay. Difficulties associated with estimating these parameters using field data complicate the identification and measurement of holdout behavior, and for this reason previous research on the land-assembly problem has been primarily theoretical. (4) This article uses experimental methods to examine holdout behavior in laboratory bargaining games that involve multi-person groups, complementary exchanges, and holdout externalities. While there is a large literature on laboratory bargaining behavior, the vast majority of these studies examine behavior in two-person games involving a single "buyer" (or proposer) and a single "seller" (or responder). While one party may "holdout" in multi-period bargaining environments (see, for example, McKelvey and Palfrey 1995; Gneezy, Haruvy, and Roth 2003) in hopes of receiving a larger payoff, there are no co-dependent transactions. Thus, while there may be costly delay in simple two-person bargaining environments, no holdout externalities of the kind commonly associated with land-assembly-type problems are present. Some experimental analyses of Coasian bargaining (for example, Hoffman and Spitzer 1986; Harrison et al. 1987) include larger groups but lack the critical interdependence of transactions necessary for holdout externalities. This research, therefore, provides an important link between the theoretical analysis of holdout developed extensively in the land-assembly literature and the experimental analysis of behavior in bargaining games.

    We distinguish the holdout problem from a related "hold-up" problem (Williamson 1975; Klein, Crawford, and Alchian 1978; Ellingsen and Johannesson 2004; Dawid and MacLeod 2008), which refers to the case when an upstream agent must make a costly investment in the first stage of a game that is only of use to a single downstream agent in the second stage. In such cases, a first-period investment can be held up in a second period by the downstream agent in an attempt to extract a greater share of the total surplus generated by the investment. The ex post commitment problem inherent in the hold-up problem can lead to inefficiently low investment in the first stage of the game.

    If a land assembler must purchase a set of required parcels sequentially, then initial purchases may represent an investment that is not easily reversible, or reversible only at a considerable loss to the assembler. In such cases, both a hold-up and a holdout problem exist in the bargaining game as landowners who have not yet sold may ex post exploit the assembler's previous investment. However, if the assembler can write contingent contracts, such that no purchases occur unless agreement is reached with all landowners, then only a holdout problem exists. We model only the latter situation.

    We examine the holdout problem with six experimental treatments that vary the bargaining institution, the number of bargaining periods, and the cost associated with delay. Our results demonstrate that holdout is common across institutions and is, on average, a payoff-improving strategy for responders, despite theoretical predictions. Initial offers-to-buy decrease and demands-to-sell increase in multi-period bargaining treatments relative to a single-period treatment. Responders are also more likely to reject a given offer in multi-period treatments. Imposing delay costs causes offers-to-buy to rise, demands-to-sell to fall, a higher probability of responders to accept a given offer or demand, and less overall holdout. Importantly, nearly all exchanges eventually occur in our multi-period treatments, leading to higher overall efficiency relative to the single-period treatments, both with and without delay costs.

    However, caution should be exercised when considering the implications of our results for the eminent domain question. Our treatments have a very small number of sellers and complete and perfect information, characteristics that are unlikely to be present in the field. Therefore, the current study should be viewed as an initial empirical investigation of holdout behavior and costs, leaving many important questions unanswered. The potential for eminent domain to improve social welfare in the field depends upon the costs of delay relative to the costs of potentially inefficient land transfers and the disincentive effects of weakened property rights when eminent domain is used; the prospect of eminent domain may also increase bargaining delay if buyers expect to pay less under eminent domain transfer compared to the free-market transfer of property. For example, Munch (1975) demonstrates that the prospect of eminent domain tends to reduce some property values, leading to eminent domain prices below market value. These issues can only be resolved through further study.

    The remainder of the article is organized as follows. In section 2 we describe the basic model that motivates the experimental design. Section 3 presents the experimental treatments and provides equilibrium predictions. Experimental results are given in section 4, followed by concluding remarks in section 5.

  2. Modeling Framework

    Following Menezes and Pitchford (2004b) and Miceli and Segerson (2007), consider a simple model in which a single risk-neutral agent (the buyer) wishes to purchase N complementary units of a good from N other independent risk-neutral agents (the sellers). The units can be interpreted as intermediate inputs into the production of a large project. Each seller i has one unit for sale and incurs a cost [c.sub.i] for this unit. The value of the project to the buyer is V if N input units can be acquired but is zero otherwise. Let the buyer's valuation and the sellers' costs be such that

    [N.summation over (i=1)] [c.sub.i]

    indicating that there is an economic surplus generated by the project.

    Assuming N input units can be acquired, the payoff to the buyer is

    (V - [N.summation over (i=1)] [p.sub.i]), (2)

    where [p.sub.i] is the price paid for unit i, and each seller i receives a payoff ([p.sub.i] - [c.sub.i]). Assume the buyer may write contingent contracts such that no sales occur (and, therefore, all parties receive a payoff of zero) if any of the required input units are not purchased.

    We suppose that bargaining takes place between the buyer and the...

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