arXiv subjects

Yixian Zhu

Publications and source records attributed to Yixian Zhu.

3 recordsLinked to original sources

arXiv2022

An Experimental Study on Learning Correlated Equilibrium in Routing Games

We study route choice in a repeated routing game where an uncertain state of nature determines link latency functions, and agents receive private route recommendation. The state is sampled in an i.i.d. manner in every round from a publicly known distribution, and the recommendations are generated by a randomization policy whose mapping from the state is known publicly. In a one-shot setting, the agents are said to obey recommendation if it gives the smallest travel time in a posteriori expectation. A plausible extension to repeated setting is that the likelihood of following recommendation in a round is related to regret from previous rounds. If the regret is of satisficing type with respect to a default choice and is averaged over past rounds and over all agents, then the asymptotic outcome under an obedient recommendation policy coincides with the one-shot outcome. We report findings from an experiment with one participant at a time engaged in repeated route choice decision on computer. In every round, the participant is shown travel time distribution for each route, a route recommendation generated by an obedient policy, and a rating suggestive of average experience of previous participants with the quality of recommendation. Upon entering route choice, the actual travel times are revealed. The participant evaluates the quality of recommendation by submitting a review. This is combined with historical reviews to update rating for the next round. Data analysis from 33 participants each with 100 rounds suggests moderate negative correlation between the display rating and the average regret, and a strong positive correlation between the rating and the likelihood of following recommendation. Overall, under obedient recommendation policy, the rating converges close to its maximum value by the end of the experiments in conjunction with very high frequency of following recommendations.

cs.GT↗

arXiv2022

Convergence in a Repeated Non-atomic Routing Game with Partial Signaling

We study the following repeated non-atomic routing game. In every round, nature chooses a state in an i.i.d. manner according to a publicly known distribution, which influences link latency functions. The system planner makes private route recommendations to participating agents, which constitute a fixed fraction, according to a publicly known signaling strategy. The participating agents choose between obeying or not obeying the recommendation according to cumulative regret of the participating agent population in the previous round. The non-participating agents choose route according to myopic best response to a calibrated forecast of the routing decisions of the participating agents. We show that, for parallel networks, if the planner's signal strategy satisfies the obedience condition, then, almost surely, the link flows are asymptotically consistent with the Bayes correlated equilibrium induced by the signaling strategy.

eess.SY↗

arXiv2021

Information Design in Non-atomic Routing Games with Partial Participation: Computation and Properties

We consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. The agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signaling policy respectively. The remaining agents choose route according to Bayes Nash flow with respect to the prior. We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency over all public or obedient private signaling policies. For a fixed flow induced by non-participating agents, design of an optimal private signaling policy is shown to be a generalized problem of moments for polynomial link latency functions, and to admit an atomic solution with a provable upper bound on the number of atoms. This implies that, for polynomial link latency functions, information design can be equivalently cast as a polynomial optimization problem. This in turn can be arbitrarily lower bounded by a known hierarchy of semidefinite relaxations. The first level of this hierarchy is shown to be exact for the basic two link case with affine latency functions. We also identify a class of private signaling policies over which the optimal social cost is non-increasing with increasing fraction of participating agents for parallel networks. This is in contrast to existing results where the cost of participating agents under a fixed signaling policy may increase with their increasing fraction.

cs.GT↗