Simulations on Correlated Behavior and Social Learning

It has been widely accepted that herding is the consequence of mimetic responses by agents interacting locally on a communication network. In extant models, this communication network linking agents, by and large, has been assumed to be fixed. In this paper we allow it to evolve endogenously by enabling agents to adaptively modify the weights of their links to their neighbours by reinforcing 'good' advisors and breaking away from 'bad' advisors with the latter being replaced randomly from the remaining agents. The resulting network not only allows for herding of agents, but crucially exhibits realistic properties of socio-economic networks that are otherwise difficult to replicate: high clustering, short average path length and a small number of highly connected agents, called "gurus". These properties are now well understood to characterize 'small world networks' of . + We are grateful for discussions with Sanjeev Goyal and Fernando Vega Redondo. 1 Examples of socio-economic networks include the world wide web, co-author relationships among academics, trade networks, criminal associations, airline routing etc. See also Newman (2002). 2 It is this property that gives rise to the notion of a 'small world'. The most popular manifestation of this is known as "six degrees of separation" coined by the Stanley Milgram (1967) stating that most pairs of people in the United States can be connected through a path of only about six acquaintances. 3 The very large literature on local interaction economic models (see, that comes under the rubric of social dynamics for the study of the diffusion of innovation, information or norms is based on the Liggett/Ising framework originally adapted for economic analysis by . This framework treats local feedback effects as a stochastic process in which the probability that a given person adopts one of two possible actions, say A or B in a given period of time, is assumed to be an increasing function of the number of his 5 The rest of the paper is organized as follows. Section 2 sets out the model of herding in a simple asset market. This motivates the framework behind the experiments that evolve realistic communication network structures that influence trader behaviour. Section 3 gives some results from network theory that help to distinguish between the different network topologies. In particular, we give an easy 'look up' table on how the small world networks have connectivity properties which straddle the polar extremes of random networks, regular purely deterministic networks and a third category of networks called scale free networks, Barabesi and Albert (1999). Section 4 reports the results of the experiments. The conditions under which guru effects and star/hub formations emerge are carefully documented here. We also discuss here the conditions in our model that enable gurus to maximize and propagate their impact on the rest of the system. It is also found that once stable star/hub formations arise, this reduces the shortest average path length between any two random agents. The hub formation enhances the cohesiveness of the system by reducing the shortest average path length between agents relative to random graphs as network size increases and the network connections become sparse.

Herd effect of a group of players playing investment games with information exchange is studied using a multi-agent model with a static social network. Here investment game is a Parrondo game which can be considered as an investment into two slot machines, C and D, so that playing continuously on one slot machine will lose, but by suitable switching the play on these two slot machines a player can win in the long run. This strange effect is named after its inventor and is called the Parrondo effect, which has its roots in the nonequilibrium physics of Brownian ratchets. The effect can be calculated exactly using Markov chain analysis. Numerical and analytical results have shown that there are sequences of games composed of special motif that will lead to winning for individual player. When we couple the players by information exchange in a social network, we can study the impact of information on the collective behavior of the players. Specifically, we investigate herd effect via a simple model where the players can adopt one of two strategies: (I) Follow the winner or (II) Avoid the loser. We find interesting behavior of the resulted average gain of the population, depending on the susceptibility of the players being influenced by others. We observe that players using either 'Follow the winner' alone, or 'Avoid the loser' alone will lead to loss for the entire population. This particular feature of herd effect is explained and verified by numerical experiment. We then provide two distinct, though similar strategy of evolution for the population of players, communicating with the nearest neighbors in a ring type social network, so that the population can actually win with herd effect. The first strategy of evolution is to randomly mix the game plan "Follow the winner" with 'Avoid the loser'. The second strategy of evolution is to give each player a preset probability to switch between 'Follow the winner' and 'Avoid the loser'. Despite the similarity of these two strategies of evolution in our study of herd effect, we observe difference in the gain of the population. We also provide a heuristic explanation for this difference in gain based on the probability distribution of the resident time for the player in his selected strategy.

2015

We theoretically and empirically study an incomplete information model of social learning. Agents initially guess the binary state of the world after observing a private signal. In subsequent rounds, agents observe their network neighbors' previous guesses before guessing again. Types are drawn from a mixture of learning models-Bayesian, where agents face incomplete information about others' types, and DeGroot, where agents follow the majority of their neighbors' previous period guesses. We study (1) learning features of both types in our incomplete information model; (2) what network structures lead to failures of asymptotic learning; (3) whether realistic networks exhibit such structures. We conducted lab experiments with 665 subjects in Indian villages, and 350 students from ITAM in Mexico. We conduct a reduced form analysis and then structurally estimate the mixing parameter, finding the share of Bayesian agents to be 10% and 50% in the village and student samples, respectively.

Econometrica, 2021

This paper proposes a tractable model of Bayesian learning on large random networks where agents choose whether to adopt an innovation. We study the impact of the network structure on learning dynamics and product diffusion. In directed networks, all direct and indirect links contribute to agents' learning. In comparison, learning and welfare are lower in undirected networks and networks with cliques. In a rich class of networks, behavior is described by a small number of differential equations, making the model useful for empirical work.

The American Economic Review, 2007

We analyze games on social networks where agents select one of two actions (whether or not to adopt a new technology, withdraw money from the bank, become politically active, etc.). Agents' payo¤s from each of the two actions depend on how many neighbors she has, the distribution of actions among her neighbors, and a possibly idiosyncratic cost for each of the actions. We analyze the di¤usion of behavior when in each period agents choose a best response to last period's behavior.

Industrial and Corporate Change, 1996

Advances in stochastic system analysis have opened the way to a reconsideration of the processes through which behaviors spread in a population of individuals or organizations. One peculiar phenomenon affecting diffusion is information contagion (Arthur and Lane 1994). When agents have to choose on the basis of other people's experience, rather than relying on their own direct observations, information externalities arise that drive towards the emergence of the arbitrary, stable dominance of one product over the competing one. We reproduced in controlled laboratory conditions the process of information contagion. The experiments show that when agents can only resort to the observation of other people's experience in choosing between competing alternatives, the choice process generates some peculiar features: -information contagion among subjects generates self-reinforcing dynamics, amplifying initial asymmetries of products' market shares; -this in turn produces path-dependent trajectories, highly dependent on early events in the choice sequence; -arbitrary asymmetric market shares tend to be stable in the long run, exhibiting lock-in phenomena; -agents choice criteria are heterogenous, giving rise to a mix of positive and negative feedback in the choice process, with the mix and the timing of such criteria affecting the final outcome.

Computational Economics, 2005

Population learning in dynamic economies with endogenous network formation has been traditionally studied in basic settings where agents face quite simple and predictable strategic situations (e.g. coordination). In this paper, we start instead to explore economies where the payoff landscape is very complicated (rugged). We propose a model where the payoff to any agent changes in an unpredictable way as soon as any small variation in the strategy configuration within its network occurs. We study population learning where agents: (i) are allowed to periodically adjust both the strategy they play in the game and their interaction network; (ii) employ some simple criteria (e.g. statistics such as MIN, MAX, MEAN, etc.) to myopically form expectations about their payoff under alternative strategy and network configurations. Computer simulations show that: (i) allowing for endogenous networks implies higher average payoff as compared to static networks; (ii) populations learn by employing network updating as a "global learning" device, while strategy updating is used to perform "fine tuning"; (iii) the statistics employed to evaluate payoffs strongly affect the efficiency of the system, i.e. convergence to a unique (multiple) steady-state(s); (iv) for some class of statistics (e.g. MIN or MAX), the likelihood of efficient population learning strongly depends on whether agents are change-averse in discriminating between options associated to the same expected payoff.

We report on an experiment that uses revealed preference to distinguish between rational social learning and behavioral bias. Subjects must choose between receiving a private signal or observing the past guesses of other subjects before guessing the state of the world. The design varies the persistence of the state across time. This changes whether choosing social or private information is optimal. We can therefore separate subjects who choose optimally from both those who excessively use social information ("herd animals") and those with excessive use of private information ("lone wolves"). While aggregate behavior appears unbiased, this is because the numbers of lone wolves and herd animals are approximately equal.

arXiv (Cornell University), 2022

We consider the diffusion of two alternatives in social networks using a game-theoretic approach. Each individual plays a coordination game with its neighbors repeatedly and decides which to adopt. As products are used in conjunction with others and through repeated interactions, individuals are more interested in their long-term benefits and tend to show trust to others to maximize their long-term utility by choosing a suboptimal option with respect to instantaneous payoff. To capture such trust behavior, we deploy limited-trust equilibrium (LTE) in diffusion process. We analyze the convergence of emerging dynamics to equilibrium points using mean-field approximation and study the equilibrium state and the convergence rate of diffusion using absorption probability and expected absorption time of a reduced-size absorbing Markov chain. We also show that the diffusion model on LTE under the best-response strategy can be converted to the well-known linear threshold model. Simulation results show that when agents behave trustworthy, their long-term utility will increase significantly compared to the case when they are solely self-interested. Moreover, the Markov chain analysis provides a good estimate of convergence properties over random networks.