Harold Houba

The policy bargaining model

Abstract The policy bargaining model extends the alternating offer model and captures situations in which two players interact strategically with each other over time and simultaneously negotiate for a binding joint policy to replace competition. The assumption of a non-linear Pareto frontier causes several mathematical problems which are related to non-convex bargaining problems. The necessary and sufficient conditions for uniqueness are derived and the set of subgame perfect equilibrium payoffs are fully characterized. For the prisoners dilemma a folk theorem result is obtained. Another example shows that uniqueness is also possible.

Can negotiations prevent fish wars

The standard alternating offer model is extended by integrating it with the Levhari and Mirman fish war model in order to investigate negotiations over fish quota. The disagreement actions are endogenous. The interior and linear Markov perfect equilibrium (MPE) results in immediate agreement on an efficient path of fish quota. This MPE is not analytically tractable. Numerical solutions show that patience is a disadvantage in this MPE and small differences in patience lead to large asymmetries in the bargaining outcome.

Pricing a raindrop in a process-based model: general methodology and a case study of the Upper-Zambezi

Abstract A general approach is presented to value the stocks and flows of water as well as the physical structure of the basin on the basis of an arbitrary process-based hydrological model. This approach adapts concepts from the economic theory of capital accumulation, which are based on Lagrange multipliers that reflect market prices in the absence of markets. This permits to derive a financial account complementing the water balance in which the value of deliveries by the hydrological system fully balances with the value of resources, including physical characteristics reflected in the shape of the functions in the model. The approach naturally suggests the use of numerical optimization software to compute the multipliers, without the need to impose an immensely large number of small perturbations on the simulation model, or to calculate all derivatives analytically. A novel procedure is proposed to circumvent numerical problems in computation and it is implemented in a numerical application using AQUA, an existing model of the Upper-Zambezi River. It appears, not unexpectedly, that most end value accrues to agriculture. Irrigated agriculture receives a remarkably large share, and is by far the most rewarding activity. Furthermore, according to the model, the economic value would be higher if temperature was lower, pointing to the detrimental effect of climate change. We also find that a significant economic value is stored in the groundwater stock because of its critical role in the dry season. As groundwater comes out as the main capital of the basin, its mining could be harmful.

Computing Alternating Offers and Water Prices in Bilateral River Basin Management

This contribution addresses the fundamental critique in Dinar et al. [1992, Theory and Decision 32] on the use of game theory in river basin management: People are reluctant to monetary transfers unrelated to water prices and game theoretic solutions impose a computational burden. For the bilateral alternating-offers model, a single optimization program significantly reduces the computational burden. Furthermore, water prices and property rights result from exploiting the Second Welfare Theorem. Both issues are discussed and applied to a bilateral version of the theoretical river basin model in Ambec and Sprumont [2002, Journal of Economic Theory 107]. Directions for future research are provided.

Holdouts, backdating and wage negotiations

The Haller and Holden (JET, 1990) wage bargaining model is extended to incorporate holdouts with and without work-to-rule, inefficient holdouts and backdating of new contracts. The unions most effective action inflicts the highest costs upon the firm among the credible actions. Necessary and sufficient conditions for equilibria with lengthy holdouts are derived. Backdating does not affect the bargaining positions of the parties. The settlement wage negatively depends upon the length of the holdout and this dependence does not disappear as the time between bargaining rounds vanishes. This result has implications for empirical work. Moreover, this negative effect is small and confirms empirical evidence for the Netherlands.

Saving a river: a joint management approach to the Mekong River Basin

The Mekong River Basin (MRB) is a trans-boundary river shared by six countries. The governance by the Mekong River Commission (MRC) of the Lower Mekong Basin (LMB) is weak. This study investigates the welfare effects in the year 2030 arising from strengthening the MRCs governance versus joint management of the entire MRB. Without joint management, strengthening the MRCs governance has a huge potential to achieve welfare gains and it requires that the interests of all stakeholders be equally balanced. A bargaining approach shows that the LMB has no incentive to negotiate with China and is better off strengthening the MRCs governance instead. If such strengthening could be realized, further welfare gains of joint management by a wider and stronger MRC, including China, would be very small.

Asymmetric Nash Solutions in the River Sharing Problem

We study unanimity bargaining among agents along a general river structure that is expressed by a geography matrix and who have access to limited local resources, cost functions that depend upon river inflow and own extraction, and quasi-linear preferences over water and money. Bargaining determines the water allocation and monetary transfers. We translate the legal principles of Absolute Territorial Sovereignty (ATS) and Unlimited Territorial Integrity (UTI) from International Water Law into our model. ATS and a strict interpretation of UTI result in disagreement outcomes that are feasible. And a second interpretation of UTI is translated into individual aspiration levels that are infeasible. For disagreement outcomes, we apply the asymmetric Nash bargaining solution. Common intuition that upstream and midstream countries always prefer the ATS principle to the strict UTI principle (while the opposite preference holds for the downstream country) is reversed for such countries with sufficient bargaining power. For individual aspiration levels, the agents have to compromise in order to agree and we apply the asymmetric Nash rationing solution. The participation constraints in the Nash rationing solution matter. In all cases the optimization problem is separable into two subproblems: the efficient water allocation that maximizes utilitarian welfare; and the determination of monetary transfers.

Antitrust Enforcement and Marginal Deterrence

We study antitrust enforcement in which the fine must obey four legal principles: punishments should fit the crime, proportionality, bankruptcy considerations, and minimum fines. We integrate these legal principles into an infinitely-repeated oligopoly model. Bankruptcy considerations ensure abnormal cartel profits. We derive the optimal fine schedule that achieves maximal social welfare under these legal principles. This optimal fine schedule induces collusion on a lower price making it more attractive than on higher prices. Also, raising minimum fines reduces social welfare and should never be implemented. Our analysis and results relate to the marginal deterrence literature by Shavell (1992) and Wilde (1992).

Odd man out: the proposal-making model

Abstract The proposal-making model is applied to the class of three-player/three-cake problems. The set of subgame perfect equilibria (SPEs) and the limit set of SPE payoffs as the risk of breakdown vanishes is characterized. The necessary and sufficient condition for uniqueness is derived. The results for the alternating offer model play an important role. The model always admits one stationary SPE and this equilibrium is related to a multilateral Nash solution. The stationary SPE is the coalition-proof SPE and the limit result differs from the result known for the model without risk of breakdown.

Extreme equilibria in the negotiation model with different time preferences

We study a negotiation model with a disagreement game between offers and counteroffers. When players have different time preferences, delay can be Pareto efficient, thereby violates the presumption of the Hicks Paradox. We show that all equilibria are characterized by the extreme equilibria. Making unacceptable offers supports extreme equilibria, and significantly alters the backward-induction technique to find the extreme equilibrium payoffs. A playerʼs worst equilibrium payoff is characterized by a minmax problem involving efficient equilibrium payoffs that are above the bargaining frontier, which is possible when players have sufficiently different time preferences.