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Social Choice and Welfare
Published in: Social Choice and Welfare 2/2023

31-03-2023 | Original Paper

Forward induction and market entry with an endogenous outside option

Authors: Antonio J. Morales, Javier Rodero-Cosano

Published in: Social Choice and Welfare | Issue 2/2023

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Abstract

We consider a two-player sequential game in which players first choose whether to engage in a productive (market game) or unproductive activity (contest game) and then, if both players have chosen to enter the market, they compete in prices. Both economic activities are linked because the rents in the contest game are a fraction of the market profits. Subgame perfection predicts competitive pricing and a battle-of-the-sexes reduced-form game with two asymmetric Nash equilibrium, where only one firm enters. Our experimental results reject the prediction based on backward induction but are easily explained by forward induction arguments. The payoffs from the rent-seeking activity (outside option) influence pricing behaviour and prices do not converge to marginal costs. When the size of the rent seeking activities is large, firms coordinate better on economic activities and, in the event of market competition, prices converge to full collusion.
previous article Moral awareness polarizes people’s fairness judgments
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Appendix
Available only for authorised users
Footnotes
1
In a companion paper, Morales et al (2022), we analyse the balance between productive and unproductive activities in a three-firm experiment.
 
2
In the mixed-strategy equilibrium, a duopoly in the market happens with probability \({\left(1-t\right)}^{2}\), a monopoly happens with probability \(2t\left(1-t\right)\) and no production occurs with probability \({t}^{2}\).
 
3
We do not obtain sorting as predicted by some learning models (see Duffy and Hopkins 2005) nor do we obtain alternation (Erev et al. 2010) although there is some non-significant evidence of this phenomenon in the treatment High.
 
4
We compare the entry rate to 50% because in a battle-of-the-sexes game, there are two asymmetric Nash equilibria. Assuming Nash predictions, miscoordination may originate from both players choosing different equilibria. If they randomise between both pure strategy equilibria, the level of miscoordination would be 50%. There is an additional symmetric mixed-strategy equilibrium in which players choose enter with probability \({\left(1-t\right)}^{2}\), and miscoordination occurs with probability \(1-2t\left(1-t\right)\). In both treatments, miscoordination would occur in equilibrium with probability 58%.
 
5
The dummy variable High is statistically significant in none of the four models analysed. The reason is that, in the treatment High, only in 50% of the rounds we observe both firms entering the market and engaging in price competition, so we have far fewer observations of prices in the treatment High than in the treatment Low, where all firms enter the market to compete in prices. For example, in the second half of the experiment, there are two groups where firms never compete in prices (in the treatment High), so the number of groups for the second half of the experiment is 18.
 
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Metadata
Title
Forward induction and market entry with an endogenous outside option
Authors
Antonio J. Morales
Javier Rodero-Cosano
Publication date
31-03-2023
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 2/2023
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-023-01455-5

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