The Statistical Mechanics of Strategic Interaction

By L. Blume. 1993

I study strategic interaction among players who live on a lattice. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. I examine various stochastic strategy revision processes, including (myopic) best response and stochastic choice. I discuss both stationary distributions and the limit behavior of these Markov processes. Stationary distributions are partially characterized, and the asymptotic behavior of stochastic choice for those processes whose choice rule is nearly best-response is related to equilibrium selection in symmetric 2 × 2 and n × n coordination games. Journal of Economic Literature Classification Number: C78.

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Citations in the corpus

Mean Field Multi-Agent Reinforcement Learning (2018, background): “It is worth noting that the pairwise approximation of the agent and its neighbors, while significantly reducing the complexity of the interactions among agents, still preserves global interactions between any pair of agents implicitly (Blume, 1993).”
Maximizing the spread of influence through a social network (2003, background): “Some of the earliest systematic investigations focused on data pertaining to the adoption of medical and agricultural innovations in both developed and developing parts of the world [23, 69, 79]; in other contexts, research has investigated diffusion processes for “word-of-mouth” and “viral marketin”
Cooperative Control and Potential Games (2009, methodology): “We present a learning algorithm for this class of games and demonstrate that when applied to the consensus problem, this algorithm guarantees consensus even in an environment containing arbitrary obstructions.”
Colloquium: Statistical mechanics of money, wealth, and income (2009, background): “Several economists (Blume, 1993; Durlauf, 1997; Foley, 1994; Follmer, 1974) applied statistical physics to economic problems.”
Potential Games with Continuous Player Sets (2001, background): “Blume [3, 4, 5] shows that i f players are randomly matched to play a finite player potential game, then the global maximizer of potential is the unique stochastically stable outcome when mutation probabilities are determined v ia the log-linear choice rule.”
Statistical physics of vaccination (2016, background): “Here Πi and Πj are their payoffs, while κ (0 < κ <∞) denotes the strength of selection [424, 513, 514] (note that κ is different from the imitation coefficient κ for well-mixed population in Section 8).”
The Impact of Information Provision on Agglomeration Bonus Performance: An Experimental Study on Local Networks (2014, unknown): “positive precedent effect for the choice of N , which can be attributed to strategy lock-in or strategy inertia (Blume 1993).”
Sequential Influence Models in Social Networks (2010, background): “…and the diffusion of innovations (Rogers 1995; Strang and Soule 1998); in economics, theoretical models have been developed to cast social influence as a process by which individuals in a social network tend to coordinate (or anti-coordinate) their decisions (e.g. (Blume 1993; Young 1998)).”
Human strategy updating in evolutionary games (2010, background): “[32] Blume, LE (1993) The statistical mechanics of strategic interaction.”
On the formation of interaction networks in social coordination games (2002, background): “…to have inefficient play be stochastically stable even when the efficient strategy is risk dominant, in a model where individuals completely 3 Ellison (1993) and Young (1998) also present interesting results on how the time associated with the ``long run’’ varies depending on the network…”
Discrete Choice with Social Interactions (2001, methodology): “Our analysis follows Blume (1993) and Brock (1993) in exploiting the relationship between models of discrete choice with interaction effects and a particular random fields model.”
Identification of Social Interactions (2011, unknown): “Early theoretical studies include Blume (1993), Brock (1993), Durlauf (1993) and Glaeser, Sacerdote, and 64 Scheinkman (1996).”
ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY (2002, background): “In the stochastic evolutionary model of Blume (1993, 1997) and Young (1998), these dynamics describe expected changes in the behavior of large populations of myopic agents.”