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This chapter tells the story of how the concept of Pareto efficiency was shipped from Lausanne to the modern US theory of competitive general equilibrium, focusing on the specific role of Maurice Allais. It identifies similarities in both epistemological approach and theoretical achievements realized first by Pareto, then by Allais, and finally by Debreu and Arrow and Hahn. It also shows that these similarities are not casual, since historical circumstances account for the influence of Pareto on Allais and later of Allais on Arrow and Debreu.

A serious problem in the pandemic days is that in this period many firms face difficulties with remaining on the market. It causes that the entrepreneurs do not undertake activities which could result in introducing innovations. In this context, the authors examine new mechanisms which lead competitive economy to the long-run equilibrium under the assumption that producers are change-averse.

The results have the form of theorems with rigorous proofs and provide the ideas on the way of developing the economic policy in respect of firms in the pandemic days.

As a result, the authors justify that in some cases it is worth leading an economic sector or a whole economy to the long-run equilibrium state.

The authors show that there exists a mechanism in the sense of Hurwicz which transforms the economy into an economic system being in the long-run equilibrium as well as the authors determine optimal mechanisms, under the criterion of distance minimization, in some subsets of the mechanisms designed.

The research in competitive facility location (CFL) is quite dynamic, both from a problem formulation and an algorithmic point of view. Research direction has changed immensely over the years to address various competitive challenges. This study aims to explore CFL literature to highlight these research trends, important issues and future research opportunities.

This study utilises the Scopus database to search for related CFL models and adopts a five-step systematic approach for the review process. The five steps involve (1) Article Identification and keyword selection, (2) Selection criteria, (3) Literature review, (4) Literature analysis and (5) Research studies.

The paper presents a comprehensive review of CFL modelling efforts from 1981 to 2021 to provide a depth study of the research evolution in this area. The published articles are classified based on multiple characteristics, including the type of problem, type of competition, game-theoretical approaches, customer behaviour, decision space, type of demand, number of facilities, capacity and budget limitations. The review also highlights the popular problem areas and dedicated research in the respective domain. In addition, a second classification is also provided based on solution methods adopted to solve various CFL models and real-world case studies.

The paper covers 40 years of CFL literature from the perspective of the problem area, CFL characteristics and the solution approach. Additionally, it introduces characteristics such as capacity limit and budget constraint for the first time for classification purposes.

This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.

The purpose of this study is to explore the coopetition relationships between platform owners and complementors in complementary product markets. Drawing on the coopetition theory, the authors examined the evolutionary trends of the coopetition relationships between platform owners and complementors and explore the main influence factors.

The authors used Lotka–Volterra model to analyze the coopetition relationship between platform owners and complementors, including the evolutionary trends as well as the results. Considering the feasibility of sample data collection, simulation is used to verify the effects of different factors on the evolution of coopetition relationships.

The results show that there are four possible results of the competition in the complementary products market. That comprises “winner-take-all for platform owners,” “winner-take-all for complementors,” “stable competitive coexistence” and “unstable competitive coexistence,” where “stable competitive coexistence” is the optimal evolutionary state. Moreover, the results of competitive evolution are determined by innovation subjects’ interaction parameters. However, the natural growth rate, the initial market benefits of the two innovators and the overall benefits of the complementary product markets influence the time to reach a steady state.

The study provides new insights into the entry of platform owners into complementary markets, and the findings highlight the fact that in complementary product markets, platform owners and complementors should seek “competitive coexistence” rather than “winner-takes-all.” Moreover, the authors also enrich the coopetition theory by revealing the core factors that influence the evolution of coopetition relationships, which further enhance the analysis of the evolutionary process of coopetition relationships.