Research

Working papers

Gains in evolutionary dynamics: a unifying approach to linking static and dynamic stability

Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution (formerly titled “Nonaggregable [Disaggregable] evolutionary dynamics under payoff heterogeneity”)

Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamics

General dynamic stability of evolutionary stable states. (Manuscript available upon a request.)

Excess Liquidity against predation (Stackelberg version)
Cournot version with complete proof of revelation principle: DETU Working Paper 12-01

Abstract: To study motive for excess liquidity holding, we investigate cash flows of an entrant in product market competition by explicitly considering a cash-in-advance constraint on payment of production costs. A shallow-pocket entrant may secure financing to pay these costs based on anticipated profits. However, this creates a threat of predation by a deep-pocket competitor. To block predation, the entrant must raise precautionary liquidity, by taking out a loan both larger and further in advance than is actually necessary for production. Entrants with little start-up capital become less aggressive, because the need to raise precautionary liquidity introduces an additional marginal cost of production.
Keywords: excess liquidity, predation, cash-in-advance constraint, financial contract

Revelation principle under strategic uncertainty: application to financial contracts with limited liability

Abstract: We consider a principal-agent model in which the principal can terminate the agent’s project and an outsider can affect the project’s result. Only the agent can observe the outsider’s action and sends a message to the principal. Under strategic uncertainty about the outsider’s action, sequential equilibrium is the most suitable equilibrium concept to select the robust outcome and to completely identify the underlying posterior belief. We prove the revelation principle for sequential equilibrium in such a game. Based on this revelation principle, we propose a legitimate and simple form of the limited liability constraint on a financial contract that is robust to strategic uncertainty.
Keywords: revelation principle, sequential equilibrium, strategic uncertainty, limited liability, financial contracts

Adjustment costs in optimal dynamic pricing of a network good

Abstract: We consider optimal dynamic pricing of a network good, especially participation to a platform. We find a Lyapunov function that characterizes where and how the platform size converges under the optimal dynamic pricing. The difference between the Lyapunov function and the profit in a static equilibrium can be interpreted as adjustment costs, and we can justify this interpretation by a myopic pricing scheme as an approximation. This justification suggests that recurrent adjustment of a myopic pricing scheme brings the platform to the same size in the long run as the optimal dynamic pricing.
Keywords: entry game, platform, adjustment costs, dynamic optimization, network externality

Book drafts

Introduction to formal mathematics for economic modeling, under contract with Temple University Press. (Expected to publish as an open access textbook around the end of 2020)

Target courses: “mathematics for economics” as an undergraduate advanced course; or as a graduate core course at a program where majority of students have weak math background and little or no training of abstract mathematics.

I am glad to share the book draft with any instructors/professors and receive feedback. Please contact with me (from your university e-mail address).

Publications

Refereed research articles

Evolutionary dynamics in multitasking environments (with Ryoji Sawa) Journal of Economic Behavior and Organization, in press, 2019. doi: 10.1016/j.jebo.2019.06.021

A potential game approach to modelling evolution in a connected society (with Jiabin Wu), Nature Human Behaviour, in press (published online on Apr 8, 2019), doi: 10.1038/s41562-019-0571-0

Abstract: When studying human behaviour, it is important to understand not just how individuals interact, but also interactions at the level of communities and populations. Most previous modelling of networks has focused on interactions between individual agents. Here we provide a modelling framework to study the evolution of behaviour in connected populations, by regarding subpopulations as the basic unit of interaction and focusing on the population-level connection structure. We find that when the underlying game played by individuals is a potential game, utilizing such a structure greatly simplifies analysis. In addition, according to known general results on the convergence of evolution dynamics to Nash equilibria in a potential game, our formulation provides a tractable model on behavioural dynamics in social networks that needs only conventional techniques from evolutionary game theory.

Tempered best response dynamics, International Journal of Game Theory, March 2018, Volume 47, Issue 1, pp 1–34. doi: 10.1007/s00182-017-0575-9

Abstract: We propose a new deterministic evolutionary dynamic—the tempered best response dynamic (tBRD)—to capture two features of economic decision making: optimization and continuous sensitivity to incentives. That is, in the tBRD, an agent is more likely to revise his action when his current payoff is further from the optimal payoff, and he always switches to an optimal action when revising. The tBRD is a payoff monotone selection like the replicator dynamic, which makes medium and long-run outcomes more consistent with predictions from equilibrium refinement than the BRD in some situations. The technical contribution of the tBRD is continuous sensitivity, which allows us to apply results of a system of piecewise differential equations in order to obtain conditions for uniqueness and stability of solutions.
Keywords: best response dynamic, payoff monotonicity, status-quo bias, switching costs, proper equilibrium, piecewise differential equations

Evolution of conformity preference and migration over communities (with Futao Lu), Games, 2017, 8(4), 51; doi: 10.3390/g8040051

Abstract: While conformity pressures people to assimilate in a community, an individual occasionally migrates among communities when the individual feels discomfort. These two factors cause segregation and cultural diversity within communities in the society. By embedding a migration dynamic into Kuran and Sandholm’s model (2008) of preference evolution, we build an agent-based model to see how the variance of preferences in the entire society quantitatively changes over time. We find from the Monte-Carlo simulations that, while preferences assimilate within a community, self-selected migrations enlarge the diversity of preferences over communities in the society. We further study how the arrival rate of migration opportunities and the degree of conformity pressures affect the variance of preferences. Keywords: segregation; assimilation; polarization; cultural discontents; evolutionary dynamics; conformity; simulation

Market size effects on long-run demand of a network good, Economics Bulletin, 35(4), 2015.

Abstract: We consider optimal dynamic pricing under a network externality. We construct the demand dynamic of the network good from the aggregate best response dynamic of agents who have different adoption costs. When the distribution of adoption costs is convex, expansion of potential market inevitably enlarges long-run demand.
Keywords: entry game, platform, dynamic optimization, network externality, size effects, non-concavity

Evolutionary imitative dynamics with population-varying aspiration levels (with Ryoji Sawa), Journal of Economic Theory, 154 (1), 2014. doi: 10.1016/j.jet.2014.10.001)

Abstract: We consider deterministic evolutionary dynamics under imitative revision protocols. We allow agents to have different aspiration levels in the imitative protocols where their aspiration levels are not observable to other agents. We show that the distribution of strategies becomes statistically independent of the aspiration level eventually in the long run. Thus, long-run properties of homogeneous imitative dynamics hold as well, despite heterogeneity in aspiration levels.
Keywords: Learning; Imitation; Multiple Populations; Aspiration level; Wright manifold

Interior convergence under payoff monotone selections and proper equilibrium: application to equilibrium selection, Annals of the International Society of Dynamic Games, Vol. 13, 2013. (doi:10.1007/978-3-319-02690-9_6)

Abstract: An interior convergent path in an evolutionary dynamic can be seen as a sequence of perturbed quasi-equilibria to refine an equilibrium. In this note, we investigate a variety of conditions to establish the connection between interior convergence in regular payoff monotone selections and versions of proper equilibrium and use the connection for equilibrium selection.
Keywords: evolutionary dynamics, payoff monotone selections, proper equilibrium

Other publications

Keizaigaku no Uchu (Universe of Economics), by Katsuhito Iwai and Hiroyuki Maeda, Social Science Japan Journal, 19 (2): 215-218, Oxford UP, 2016. doi:10.1093/ssjj/jyw034. (Refereed book review on a general social sciences journal on Japan studies, published in English jointly by U Tokyo and Oxford UP.)

制約付き最大化問題を解く, 経済セミナー, 662号, 日本評論社, 2011年。 Solving a maximization problem with constraints, Economic Seminar, Tokyo: Nihon Hyoronsha, No. 662, 2011. (Invited expository article on a leading introductory journal—comparable with American Economist, published in Japanese.)

ミクロ経済学:「傾き」で考える, 経済セミナー, 618号,  日本評論社, 2006年。 Microeconomics: Think with “Slopes”, Economic Seminar, Tokyo: Nihon Hyoronsha, No. 618, 2006. (Invited expository article on a leading introductory journal—comparable with American Economist, published in Japanese.)