International Society of Dynamic Games

Dynamic Games and Applications Seminar

On the Non-Uniqueness of Linear Markov Perfect Equilibria in Linear-Quadratic Differential Games: A Geometric Approach

February 22, 2024 11:00 AM — 12:00 PM (Montreal time)

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Although the possibility of multiple nonlinear equilibria in linear-quadratic differential games is extensively discussed, the literature on models with multiple linear Markov perfect equilibria (LMPEs) is scarce. And indeed, almost all papers confined to a single state (a very large majority of the application of differential games to economic problems) find a unique LMPE. This paper explains this finding and derives conditions for multiplicity based on the analysis of the phase plane in the state and the derivative of the value function. The resulting condition is applied to derive additional examples using pathways different from the (two) known ones. All these examples, more precisely, their underlying pathways, contradict usual assumptions in economic models. However, by extending the state space, we provide an economic setting (learning by doing) that leads to multiple LMPEs.

Dynamic Games and Applications Seminar

A Dynamic Analysis of Criminal Networks

February 15, 2024 11:00 AM — 12:00 PM (Montreal time)

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We take a novel approach based on differential games to the study of criminal networks. We extend the static crime network game (Ballester et al., 2006, 2010) to a dynamic setting where criminal activities negatively impact the accumulation of total wealth in the economy. We derive a Markov Perfect Equilibrium, which is unique within the class of strategies considered, and show that, unlike in the static crime network game, the vector of equilibrium crime efforts is not necessarily proportional to the vector of Bonacich centralities. Next, we conduct a comparative dynamic analysis with respect to the network size, the network density, and the marginal expected punishment, finding results in contrast with those arising in the static crime network game. We also shed light on a novel issue in the network theory literature, i.e., the existence of a voracity effect. Finally, we study the problem of identifying the optimal target in the population of criminals when the planner’s objective is to minimize aggregate crime at each point in time. Our analysis shows that the key player in the dynamic and the static setting may differ, and that the key player in the dynamic setting may change over time. (with Paola Labrecciosa and Agnieszka Rusinowska)

Dynamic Games and Applications Seminar

Impacts of Different Contracts and Policy Constraints in a Distributional Robust Approach

February 8, 2024 11:00 AM — 12:00 PM (Montreal time)

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This research tackles decentralized supply channels and proposes comprehensive solution algorithms for multi-periodic bilevel equilibrium problems. The supply channel consists of two members, an upstream member (manufacturer) and a downstream member (retailer), who assume the roles of leader and follower, respectively, in a Stackelberg game. The primary objective of the channel is to effectively manage dynamic demand, which is dependent on price history, within a multi-period time frame. Due to the price history effect on the uncertain demand, the problem turns out to be highly nested. We present a channel facing dynamic and price-dependent demand, where the demand information is incomplete, and the only information provided is the mean and the standard deviation of the demand. To address this challenge, a distributional-robust (DR) approach is proposed, which provides a lower bound on the channel’s expected profit for the problem with known distribution. We consider both periodic contracts (a subgame perfect solution) and single contract (covering all periods simultaneously). The leader’s expected payoff of a single contract, logically, is not lower than the subgame perfect result. For the follower on the other hand, we did not observe any counterexample to demonstrate that he may be worse off by using a single contract. The algorithm optimally addresses concerns related to corrective actions. It incorporates pollution capacity constraints, pollution tax, and a cap-and-trade system. Moreover, a buyback contract influence, to share the risk of leftovers optimally, is evaluated. (joint work with Leif Kristoffer Sandal)