Inefficient Cooperation Under Stochastic and Strategic Uncertainty

• DOI: 10.1177/00220027211066614
• Author: Juri Nithammer,Lisa Bruttel,Werner Güth,Andreas Orland
• Date: 01 May 2022
• Published date: 01 May 2022
• Subject Matter: Articles

Article

Journal of Conf‌lict Resolution

2022, Vol. 66(4-5) 755–782

© The Author(s) 2022

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DOI: 10.1177/00220027211066614

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Ineff‌icient Cooperation

Under Stochastic and

Strategic Uncertainty

Lisa Bruttel

1

, Werner Güth

2

, Juri Nithammer

1

, and

Andreas Orland

1

Abstract

Stochastic uncertainty can cause coordination problems that may hinder mutu ally

benef‌icial cooperation. We propose a mechanism of ex-post voluntary transfers

designed to circumvent these coordination problems and ask whether it can increase

eff‌iciency. To test this transfer mechanism, we implement a controlled laboratory

experiment based on a repeated Ultimatum Game with a stochastic endowment.

Contrary to our hypothesis, we f‌ind that allowing voluntary transfers does not lead to

an eff‌iciency increase. We suggest and analyze two major reasons for this failure: f‌irst,

stochastic uncertainty forces proposers intending to cooperate to accept high strategic

uncertainty, which many proposers avoid; second, many responders behave only

incompletely conditionally cooperatively, which hinders cooperation in future periods.

JEL-Classif‌ication: C78, C92, D74

Keywords

stochastic uncertainty, strategic uncertainty, cooperation, Ultimatum Game,

experiment

1

University of Potsdam, Department of Economics and Social Sciences, Potsdam, Germany

2

LUISS Guido Carli, Rome, Italy; and Max Planck Institute for Research on Collective Goods, Bonn, Germany

Corresponding Author:

Juri Nithammer, University of Potsdam, Department of Economics and Social Sciences, August-Bebel-Str. 89,

14482 Potsdam, Germany.

Email: juri.nithammer@uni-potsdam.de

Introduction

Bargaining under uncertainty is diff‌icult for many reasons. First, stochastic

uncertainty—uncertainty about the realization of an environmental variable—creates

coordination problems. These problems are solvable as long as the bargaining parties

can condition bargaining outcomes on the realized state of nature (Riddell, 1981),

1

but

eff‌icient solutions become harder when stochastic uncertainty coincides with other

uncertainties. See, for example, Cramton (1984,1992) who shows theoretically that

uncertainty about others’preferences leads to ineff‌iciencies in bargaining outcomes.

Often, stochastic uncertainty goes along with strategic uncertainty—uncertainty about

the behavior of others—because an increase in stochastic uncertainty for an agent

makes this agent’s behavior less predictable or forces agents into a mutual dependency.

2

Finally, both stochastic uncertainty and strategic uncertainty are often one-sided or

asymmetric among bargaining parties, for example, due to information advantages or

because of the sequential timing of decisions as in Grossman and Perry (1986).

To f‌ix ideas, let us introduce a specif‌ic example of such bargaining under stochastic

uncertainty. Suppose a union and a f‌irm meet for annual wage negotiations. There may

be conf‌licting interests, but both could benef‌it from a cooperative outcome where each

party receives a fair share of the surplus and no strike is necessary. These negotiations

take place in a stochastic environment with information asymmetries: many external

factors like shocks to the business cycle can affect the wage-increase leeway (Oderanti

et al., 2012) and f‌irms are better informed about the generated surplus than unions. It

might be benef‌icial if unions and f‌irms could arrange an additional voluntary ex-post

compensation from the f‌irms to the union members if the year goes better than initially

expected. Such bonuses are common and sizable, especially in the industrial sector

(Hashimoto, 1979;Byungnamlee and Rhee, 1996), for example, in car manufacturing

(Isidore, 2017).

There are many other examples: stochastic uncertainty may challenge the collusion

of f‌irms with uncertain demand (Green and Porter, 1984). In international relations,

external shocks such as election outcomes can inf‌luence trade negotiations (Milner and

Rosendorff, 1997), and uncertainty about a temperature threshold can impede suc-

cessful climate negotiations (Milinski et al., 2011;Barrett and Dannenberg, 2012,2014,

2017). Some aspects of a country’s decision to join a supranational organization such as

the European Union can also be understood as bargaining under stochastic uncertainty.

3

Our study contributes to a better understanding of the mechanisms potentially

affecting eff‌icient cooperation in situations like negotiations between unions and

f‌irms.

4

We replicate the main features of bargaining under uncertainty in a model based

on the Ultimatum Game (Güth et al., 1982) with a stochastic endowment (see also the

related study by Güth et al. 2020). Then, we test whether a mechanism of voluntary ex-

post transfers can mitigate the problem. In our version of the Ultimatum Game, a

proposer (i.e., a union) makes a claim in absolute units without knowing the en-

dowment’s eventual size (i.e., the surplus). Then, the responder (i.e., a f‌irm), after

learning the size of the endowment, can either accept or reject the resulting offer. The

756 Journal of Conf‌lict Resolution 66(4-5)