Games and Economic Behavior 75 (2012) 538–554
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Games and Economic Behavior
www.elsevier.com/locate/geb
Stochastic stability in best shot network games
Leonardo Boncinelli
a
,∗
,PaoloPin
b
a
Dipartimento di Scienze Economiche, Università degli Studi di Pisa, Via Cosimo Ridolfi 10, 56124 Pisa, Italy
b
Dipartimento di Economia Politica e Statistica, Università degli Studi di Siena, Italy
article info abstract
Article history:
Received 13 February 2011
Available online 13 March 2012
JEL classification:
C72
C73
D85
H41
Keywords:
Networks
Best shot game
Stochastic stability
Thebestshotgameappliedtonetworksisadiscretemodelofmanyprocessesof
contribution to local public goods. It generally has a wide multiplicity of equilibria
that we refine through stochastic stability. We show that, depending on how we define
perturbations – i.e., possible mistakes that agents make – we can obtain very different sets
of stochastically stable states. In particular and non-trivially, if we assume that the only
possible source of error is that of a contributing agent that stops doing so, then the only
stochastically stable states are Nash equilibria with the largest contribution.
©
2012 Elsevier Inc. All rights reserved.
1. Introduction
In this paper we will look at a stylized game of contribution to a discrete local public good where the range of exter-
nalities is defined by a network. With small probability players may fail to play their best response and we analyze which
equilibria are most stable to such errors. In particular, we show that the nature of the mistake has a fundamental role in
determining characteristics of such stable equilibria.
Let us start with an example.
Example 1. Ann, Bob, Cindy, Dan and Eve live in a suburb of a big city and they all have to take private cars in order to
reach downtown every working day. They could share the car but they are not all friends: Ann and Eve do not know each
other but they both know Bob, Cindy and Dan, who also don’t know each other. The network of relations is shown in Fig. 1.
In a one-shot equilibrium (the first working day) they will end up sharing cars. Any of our characters would be happy to
give a friend a lift, but we presume here that non-linked people do not know each other and would not offer one another
a lift. No one would take the car if a friend is doing so, but someone would be forced to take it if all her friends are not
doing so. There is a less congested equilibrium in which Ann and Eve take the car (and the other three somehow get a lift),
and a more polluting one in which Bob, Cindy and Dan take their car (offering Ann and Eve a lift, who will choose one of
them).
Imagine being in the less congested equilibrium. Now suppose that, even if they all agreed on how to manage the trip,
in the morning Ann finds out that her car engine is broken and cannot start it. She then calls her three friends, who are
however not planning to take their cars and cannot offer her a lift. As Ann does not know Eve, and Eve is the only one left
*
Corresponding author. Fax: +39 050 221 6384.
E-mail addresses: l.boncinelli@ec.unipi.it (L. Boncinelli), paolo.pin@unisi.it (P. Pin).
0899-8256/$ – see front matter
©
2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.geb.2012.03.001