Knowing one’s future preferences: A correlated agent model with Bayesian updating
| Author | Curtis S Signorino,Taehee Whang,Muhammet A Bas |
| Date | 01 January 2014 |
| DOI | 10.1177/0951629813482054 |
| Published date | 01 January 2014 |
| Subject Matter | Articles |
Article
Knowing one’s future
preferences: A correlated
agent model with Bayesian
updating
Journal of Theoretical Politics
2014, Vol 26(1) 3–34
©The Author(s) 2013
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DOI:10.1177/0951629813482054
jtp.sagepub.com
Muhammet A Bas
Department of Government, Harvard University, Harvard, MA, USA
Curtis S Signorino
Department of Political Science, University of Rochester, Rochester, NY, USA
Taehee Whang
Division of International Studies, Korea University, Seoul, Korea
Abstract
We generalize two classes of statistical sequential incomplete information games: (1) those
resembling typical signaling games, in which a single agent represents each player, allowing for
information to be revealed about future play; and (2) those in which each player is represented
by a set of independent agents, where moves do not reveal private information. The generalized
model we develop, the Correlated Agent Model, relies on a parameter, ρ, which denotes the corre-
lation between two agents’ private information, i.e. the extent to which a player knows the future
private component of her preferences. The independent agent and single agent models are special
cases, where ρ=0 and ρ=1, respectively. The model also allows 0 < ρ< 1, a class of games which
have not yet been considered. We apply the model to crisis bargaining and demonstrate how to
estimate ρ, as well as parameters associated with utilities.
Keywords
Correlated preferences; fully structure; strategic choice models; structural statistical models
1. Introduction
How do state leaders, members of Congress, voters, or consumers know whattheir future
preferences will be? In most applications of game theory to political behavior, researchers
Corresponding author:
Taehee Whang, Division of International Studies, Korea University, 529 International Studies Hall, Anam-
dong, Seongbuk-gu, Seoul 136-701, Korea.
Email: twng@korea.ac.kr
4Journal of Theoretical Politics 26(1)
generally assume that decision makers know their own future preferences with complete
certainty. While this assumption seems reasonable in some cases (e.g. whena small num-
ber of decisions will be made over a short period of time), there may be other situations
where it is implausible (e.g. when decisions will be made over a long period of time).
In this paper, we examine future preferences and signaling in the context of statistical
games. We develop a new approach (a Correlated Agent Model (CAM)) that generalizes
two major classes of models with private information. We demonstrate how to conduct
statistical estimation using this new approach and apply these techniques to international
crisis bargaining.
Current statistical models for crisis bargaining entail either traditional game-theoretic
assumptions (Lewis and Schultz, 2003;Wand, 2006; Whang, 2010b; McLean and
Kuberski, 2013) or ‘independent agent’ assumptions (Leblang, 2003; Signorino, 2003;
Signorino and Tarar, 2006; Gent, 2007; Bas et al., 2008; Carter, 2010; McLean and
Whang, 2010; Bas, 2013). These approaches differ in what they assume about play-
ers’ uncertainty concerning their own preferences. Traditional game-theoretic models
assume that each player completely knows at every point in the game how much she will
value the outcomes in the model, no matter how far in the future those outcomes are. In
contrast, many recent stochastic games (e.g. McKelvey and Palfrey’s Quantal Response
Equilibrium (McKelvey and Palfrey, 1995, 1998) and Signorino’s Nash-based strategic
probit models (Signorino, 1999, 2003)) take an independent agent approach. Here, each
player is represented by a different agent for each information set. A player’s agents
share the same average utility for outcomes, but have different private components that
are unobserved by her fellow agents. This assumption makes intuitive sense whenmoves
are temporally distant, e.g. I may not knowexactly how, at some point in the future, I will
value a given outcome. This assumption is also realistic when wehave a reason to expect
changes in a player’s agents, i.e. when we have reason to believe that a current agent
and a successor agent will differently value a given outcome. Finally, it is reasonable to
have the independent agent assumption when there are unexpected events or exogenous
shocks in the course of the game that alter the utility evaluation of players.
Crucially, these two models lead to distinct implications regarding the ability of
players to signal their resolve and learn from the actions of opponent players. The tra-
ditional Bayesian models allow each player to update his/her initial beliefs in the game.
Since players know their own private information before the game begins, the informed
player is capable of signaling his/her true ‘type’ and the other players fully adjust their
prior assessment of their opponent’s type and actions accordingly.The independent agent
assumption, on the other hand, implies that playersdo not lear n from each other’s moves,
since private information for each agent is unknown to, and independent of, that player’s
other agents farther down the tree.
In many important contexts, e.g. international conflicts involving territorial disputes,
economic sanctions, or military interventions, the extent to which actors have correct
understanding of their own payoffs down the game tree remains an empirical question.
Rather than pitting these approaches against each other as the only two options, and as
mutually exclusive options, wedevelop a more general approach, the CAM, that contains
each as a special case and allows us to estimate the extent to which actors know their
future preferences.
Bas et al. 5
Figure 1. Two-player signaling game.
The remainder of this paper proceeds as follows. In the next section, we set up a
theoretical model that generalizes both the traditional Bayesian model and the inde-
pendent agent model. Following that, we derive equilibrium probabilities and develop
a maximum likelihood estimator based on this more general model. We then present an
application of our statistical model to international crisis bargaining, using data from
Lewis and Schultz (2005).
2. Future preferences and correlated agents
Game-theoretic models of signaling have been used extensively in the field of interna-
tional relations. Whether the topic is crisis bargaining (Morrow, 1989; Ramsay, 2004),
deterrence (Powell, 1990; Fearon, 2002), crisis escalation and inter-state conflict (Fearon,
1997; Slantchev, 2005), the role of domestic politics in foreign policy choices (Fearon,
1994a; Mo, 1995; Schultz, 1998), terrorism (Overgaard, 1994; Arce and Sandler, 2010),
or economic sanctions (Martin, 1993; Drezner, 1998), scholars have employed signaling
models to develop theories regarding the role uncertainty plays in strategic interactions,
and what tools and mechanisms are available for actors to reduce this uncertainty or to
exploit it.
A very simple but functional version of a game involving signaling and belief updat-
ing is presented in Figure 1. Owing to the simplicity of this model and its ability to
fully capture the essence of signaling and belief updating, discrete-choice models with
the same or very similar game structures have been used extensively in the literature
(Fearon, 1994b; Smith, 1999; Schwebach, 2000; Schultz, 2001; Fearon, 2002; Lewis and
Schultz, 2003; Lacy and Niou, 2004; Lewis and Schultz, 2005; Kurizaki, 2007; Esarey
et al., 2008; Fey and Ramsay, 2011). Owing to these desirable properties, we will also
use this model to develop the statistical estimator in the next section.
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