arXiv subjects

Bonan Ni

Publications and source records attributed to Bonan Ni.

4 recordsLinked to original sources

arXiv2024

Stackelberg vs. Nash in the Lottery Colonel Blotto Game

Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these dynamics, we represent the Lottery Colonel Blotto game as a Stackelberg game, in which one player, the leader, commits to a strategy first, and the other player, the follower, responds. We derive the Stackelberg equilibrium for this game, formulating the leader's strategy as a bi-level optimization problem. To solve this, we develop a constructive method based on iterative game reductions, which allows us to efficiently compute the leader's optimal commitment strategy in polynomial time. Additionally, we identify the conditions under which the Stackelberg equilibrium coincides with the Nash equilibrium. Specifically, this occurs when the budget ratio between the leader and the follower equals a certain threshold, which we can calculate in closed form. In some instances, we observe that when the leader's budget exceeds this threshold, both players achieve higher utilities in the Stackelberg equilibrium compared to the Nash equilibrium. Lastly, we show that, in the best case, the leader can achieve an infinite utility improvement by making an optimal first move compared to the Nash equilibrium.

cs.GT↗

arXiv2024

Multiplayer General Lotto game

In this paper, we investigate the multiplayer General Lotto game across multiple battlefields, a significant variant of the Colonel Blotto game. In this version, each player employs a probability distribution for resource allocation, ensuring that their expected expenditure does not exceed their budget. We first establish the existence of the Nash equilibrium in a general setting, where players' budgets are asymmetric and the values of the battlefields are heterogeneous and asymmetric among players. Next, we provide a detailed characterization of the Nash equilibrium for multiple players on a single battlefield. In this characterization, we observe that the upper endpoints of the supports of players' equilibrium strategies coincide, and that the minimum value of a player's support above zero inversely correlates with his budget. We demonstrate the uniqueness of Nash equilibrium over a single battlefield in some scenarios. In the multi-battlefield setting, we prove that there is an upper bound on the average number of battlefields each player participates in. Additionally, we provide an example demonstrating the non-uniqueness of the Nash equilibrium in the context of multiple battlefields with multiple players. Finally, we present a solution for the Nash equilibrium in a symmetric case.

cs.GT↗

arXiv2023

Sequential Persuasion Using Limited Experiments

Bayesian persuasion and its derived information design problem has been one of the main research agendas in the economics and computation literature over the past decade. However, when attempting to apply its model and theory, one is often limited by the fact that the sender can only implement very restricted information structures. Moreover, in this case, the sender can possibly achieve higher expected utility by performing a sequence of feasible experiments, where the choice of each experiment depends on the outcomes of all previous experiments. Indeed, it has been well observed that real life persuasions often take place in rounds during which the sender exhibits experiments/arguments sequentially. We study the sender's expected utility maximization using finite and infinite sequences of experiments. For infinite sequences of experiments, we characterize the supremum of the sender's expected utility using a function that generalizes the concave closure definition in the standard Bayesian persuasion problem. With this characterization, we first study a special case where the sender can use feasible experiments to achieve the optimal expected utility of the standard Bayesian persuasion without feasibility constraints, which is a trivial utility upper bound, and establish structural findings about the sender's optimal sequential design in this case. Then we derive conditions under which the sender's optimal sequential design exists; when an optimal sequential design exists, there exists an optimal design that is Markovian, i.e., the choice of the next experiment only depends on the receiver's current belief.

cs.GT↗

arXiv2022

Characterization of Incentive Compatibility of an Ex-Ante Constrained Player

We consider a variant of the standard Bayesian mechanism, where players evaluate their outcomes and constraints in an ex-ante manner. Such a model captures a major form of modern online advertising where an advertiser is concerned with her/his expected utility over a time period and her/his type may change over time. We are interested in the incentive compatibility (IC) problem of such Bayesian mechanism. Under very mild conditions on the mechanism environments, we give a full characterization of IC via the taxation principle and show, perhaps surprisingly, that such IC mechanisms are fully characterized by the so-called auto-bidding mechanisms, which are pervasively fielded in the online advertising industry.

cs.GT↗