We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash market equilibria and other optimal strategies...

We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress...

The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an...

We consider a simple market where a vendor offers multiple variants of a certain product and preferences of both the vendor and potential buyers are heterogeneous and possibly even antagonistic. Optimization of the joint benefit of the vendor and the buyers turns the toy market into a...

We introduce a fully probabilistic framework of consumer product choice based on quality assessment. It allows us to capture many aspects of marketing such as partial information asymmetry, quality differentiation, and product placement in a supermarket.

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth...

When assets are correlated, benefits of investment diversification are reduced. To measure the influence of correlations on investment performance, a new quantity - the effective portfolio size - is proposed and investigated in both artificial and real situations. We show that in most cases, the...

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that...

We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash market equilibria and other optimal strategies...