Prevailing accounts in both multi-agent AI and the social sciences explain social structure through top-down abstractions-such as institutions, norms, or trust-yet lack simulateable models of how such structures emerge from individual behavior. Ethnographic and archaeological evidence suggests that reciprocity served as the foundational mechanism of early human societies, enabling economic circulation, social cohesion, and interpersonal obligation long before the rise of formal institutions. Modern financial systems such as credit and currency can likewise be viewed as scalable extensions of reciprocity, formalizing exchange across time and anonymity. Building on this insight, we argue that reciprocity is not merely a local or primitive exchange heuristic, but the scalable substrate from which large-scale social structures can emerge. We propose a three-stage framework to model this emergence: reciprocal dynamics at the individual level, norm stabilization through shared expectations, and the construction of durable institutional patterns. This approach offers a cognitively minimal, behaviorally grounded foundation for simulating how large-scale social systems can emerge from decentralized reciprocal interaction.

We describe the sample paths of the stochastic field $F = F_t(v,x,q)$ of aggregate utilities parameterized by Pareto weights $v$ and total cash amounts $x$ and stocks' quantities $q$ in an economy. We also describe the sample paths of the stochastic field $G = G_t(u,y,q)$, which is conjugate to $F$ with respect to the saddle arguments $(v,x)$, and obtain various conjugacy relations between these stochastic fields. The results of this paper play a key role in our study of a continuous-time price impact model.

We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter $T$ which plays the role of the temperature in physics. We show that there is a critical value of $T$, say $T_c$, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. We have considered three models: $q=3$ ( sell, buy, wait), $q=5$ (5 states between absolutely buy and absolutely sell), and $q=\infty$. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time $t_1$ and removed at the time $t_2$. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. Many striking results are obtained. In particular we show that the price strongly fluctuates near $T_c$ and there exists a critical value $H_c$ above which the boosting effect remains after $H$ is removed. This happens only if $H$ is applied in the critical region. Otherwise, the effect of $H$ lasts only during the time of the application of $H$. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time.

Emerging markets such as India provide investors with returns far greater than those in developed markets; taking the average returns from the period 1995 to 2014 the returns are 4.714% to 3.276% of the developed market. The majority of emerging markets commenced joining with the capital market of the world, thus allowing a huge inflow of capital which in turn paved the path for economic growth. Even though the emerging markets provide high returns these may also be an indication of a bubble formation. Detection of a bubble is a tedious task primarily due to the fundamental value of the security being uncertain, and the randomness of the fundamentals of the market makes detecting bubbles an arduous task. Ratios that foretold the financial crisis of 2007- Market Capitalization to GDP, Price to Earnings Ratio, Price to Book Value, Tobins Q. Data is collected from 1999-2000 from various Indian indices such as NIFTY 50, NIFTY NEXT 50, NIFTY BANK, NIFTY 500 S and PBSE SENSEX, S and P BSE 100. The paper utilizes the ratios mentioned above to detect and backtrack various bubble episodes in the Indian market; the methodology used is the Philips et al 2015 right-tailed unit test. The paper is also inclined to take steps to mitigate the effects of a bubble by amending the financial policies and the monetary liquidity of the financial system.

Eleyele Lake has enormous economic importance as it is completely surrounded by various communities which discharge their domestic waste directly into the lake. This alters the physical, chemical and biological characteristics of the lake. It is essential to assess the water for its various usage. Twelve (12) samples were collected from various locations of the lake and analysed. Some physical parameters (electrical conductivity, Total Dissolved Solids, Ph and temperature were determined in-situ. The rest of the sample was taken to the laboratory for various chemical analysis and the results were compared to the WHO standards. The chemical extent of the contamination was determined by the contamination factor, degree of contamination and Geo-Accumulation Index. The physical parameters show that the TDS has an average of 122.2ppm and EC was uniform throughout the various points of reading suggesting that the lake is fresh water. The pH averaged at 72, temperature at 27.2 degrees. The selected trace element falls within the WHO acceptable limits. Their contamination indices showed that Ba, Co, Cs, Cu, Mo, Rb, Sr and Zn are generally less than one depicting their geogenic origin. The high degree of contamination is influenced by high levels of Al and Fe due to human activities and industrial waste disposal and can lead to anemia, osteomalacia (brittle or soft bones), cardiac arrest, stomach problems, nausea, and hemochromatosis. Thus, Eleyele lake is not advisable for consumption.

The commentators have brought a wealth of new perspectives to the question of how culture evolves. Each of their diverse disciplines--ranging from psychology to biology to anthropology to economics to engineering--has a valuable contribution to make to our understanding of this complex, multifaceted topic. Though the vast majority of their comments were supportive of my approach, it is natural that a reply such as this focus on points where my views differ from that of the commentators. ... I conclude by saying that I am grateful to the commentators for their diverse perspectives and insights, their overall support for the project, and provocative ideas for where to go from here. Clearly there are many fascinating avenues to explore as we move forward on our quest to understand how culture evolves.

Universal power laws have been scrutinised in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL posits that the average price impact $I$ follows a power law with respect to transaction volume $Q$, such that $I(Q) \propto Q^δ$ with $δ\approx 1/2$. Some researchers argue that the exponent $δ$ should be system-specific, without universality. Conversely, others contend that $δ$ should be exactly $1/2$ for all stocks across all countries, implying universality. However, resolving this debate requires high-precision measurements of $δ$ with errors of around $0.1$ across hundreds of stocks, which has been extremely challenging due to the scarcity of large microscopic datasets -- those that enable tracking the trading behaviour of all individual accounts. Here we conclusively support the universality hypothesis of the SRL by a complete survey of all trading accounts for all liquid stocks on the Tokyo Stock Exchange (TSE) over eight years. Using this comprehensive microscopic dataset, we show that the exponent $δ$ is equal to $1/2$ within statistical errors at both the individual stock level and the individual trader level. Additionally, we rejected two prominent models supporting the nonuniversality hypothesis: the Gabaix-Gopikrishnan-Plerou-Stanley and the Farmer-Gerig-Lillo-Waelbroeck models (Nature 2003, QJE 2006, and Quant. Finance 2013). Our work provides exceptionally high-precision evidence for the universality hypothesis in social science and could prove useful in evaluating the price impact by large investors -- an important topic even among practitioners.

This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in high-frequency financial economics. Different with most existing literature on methodological research about developing various RL methods for market making problem, our work is a pilot to provide the theoretical analysis. We target the effects of sampling frequency, and find an interesting tradeoff between error and complexity of RL algorithm when tweaking the values of the time increment $Δ$ $-$ as $Δ$ becomes smaller, the error will be smaller but the complexity will be larger. We also study the two-player case under the general-sum game framework and establish the convergence of Nash equilibrium to the continuous-time game equilibrium as $Δ\rightarrow0$. The Nash Q-learning algorithm, which is an online multi-agent RL method, is applied to solve the equilibrium. Our theories are not only useful for practitioners to choose the sampling frequency, but also very general and applicable to other high-frequency financial decision making problems, e.g., optimal executions, as long as the time-discretization of a continuous-time markov decision process is adopted. Monte Carlo simulation evidence support all of our theories.