In a social group, some information is shared by everyone and other information is known only to some members. For example, when analyzing the interactions of college students’ academic performance, it is not likely that a student knows the IQ and/or SAT scores of all the other students in the class. Therefore, it is practical to incorporate incomplete information into a model that is used to study the interactions of individuals within any social grouping. Moreover, under different information structures, an individual will form different conditional expectations about the behavior of another group member.
“On one hand, the more information an individual has, the more precise that person’s prediction will be,” noted Lung-Fei Lee, Ph.D., a professor of economics at The Ohio State University. “On the other, the correlation of that person’s behavior with those of other individuals depends on the realizations of the publicly known characteristics and the privately known features. As a result, the intensity of interactions of behaviors of individuals in a social group will vary with the relevant information structure.”
To account for incomplete information in behavior models, researchers determine that the actions of one individual is influenced by that person’s expectations of behaviors of the rest of the people in a group, where the expectations are conditional upon the individual’s information set. By using a variable to represent those expectations, researchers can model social interactions of various types of behaviors. Moreover, since it can be assumed that it is the conditional expected behaviors that produce the variable for an individual’s behavioral responses, scientists can investigate the influence of incomplete information on social interactions.
Lee and doctoral student Chao Yang are analyzing the model as a simultaneous-move game with incomplete information. The observed data is viewed as the outcome of a Bayesian Nash Equilibrium (BNE) – a strategy profile and player beliefs about other players that maximizes the expected payoff.
“The equilibrium can be solved via the projection method, whereby we use linear combinations of the base functions to approximate the expectation functions and solve the coefficients of those linear combinations using the equilibrium condition,” explained Lee. “Although the projection method helps alleviate much of the computation burden, the model estimation is still computationally expensive, and we are using Ohio Supercomputer Center systems for Monte Carlo experiments to analyze various behaviors, information structures and network associations.”
Project Lead: Lung-Fei Lee, The Ohio State University
Research Title: Social interactions and incomplete information: A game theoretical approach
Funding Source: The Ohio State University