Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable -- which plays a role similar to price -- whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the ``thermodynamic'' limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even ``infinitesimally'' for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a ``price taker'' behavior if agents account for their market impact.Comment: 38 pages + 5 figures (needs elsart.sty). New results adde

Query Complexity of Approximate Equilibria in Anonymous Games

We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query complexity}, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by \cite{bfh09, dp14}. Our main result is a new randomized query-efficient algorithm that finds a $O(n^{-1/4})$-approximate Nash equilibrium querying $\tilde{O}(n^{3/2})$ payoffs and runs in time $\tilde{O}(n^{3/2})$. This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that $\Omega(n \log{n})$ payoffs must be queried in order to find any $\epsilon$-well-supported Nash equilibrium, even by randomized algorithms

Strategy correlations and timing of adaptation in Minority Games

We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach a la De Dominicis we compute the phase diagram and the behaviour of batch and on-line games with correlated strategies, complementing exisiting replica studies of their statics. It is shown that the timing of adaptation can be relevant; while conventional games with uncorrelated strategies are nearly insensitive to the choice of on-line versus batch learning, we find qualitative differences when anti-correlations are present in the strategy assignments. The available standard approximations for the volatility in terms of persistent order parameters in the stationary ergodic states become unreliable in batch games under such circumstances. We then comment on the role of oscillations and the relation to the breakdown of ergodicity. Finally, it is discussed how the generating functional formalism can be used to study mixed populations of so-called `producers' and `speculators' in the context of the batch minority games.Comment: 15 pages, 13 figures, EPJ styl

A short note on the problematic concept of excess demand in asset pricing models with mean-variance optimization

Referring to asset pricing models where demand is proportional to excess returns and said to be derived from a mean-variance optimization problem, the note formulates what probably is common knowledge but hardly ever made an explicit subject of discussion. This is an insufficient distinction between the desired holding of the risky asset on the part of the speculative agents, which is the solution to the optimization problem and usually directly presented as excess demand, and the desired change in this holding, which is what should reasonably constitute the excess demand on the market. The note arrives at the conclusion that in models with a market maker the story of the maximization of expected wealth should be dropped

Economics: The next physical science?

We review an emerging body of work by physicists addressing questions of economic organization and function. We suggest that, beyond simply employing models familiar from physics to economic observables, remarkable regularities in economic data may suggest parts of social order that can usefully be incorporated into, and in turn can broaden, the conceptual structure of physics.Comment: 9 pages, 6 figures, to appear in Physics Toda

Data mining for detecting Bitcoin Ponzi schemes

Soon after its introduction in 2009, Bitcoin has been adopted by cyber-criminals, which rely on its pseudonymity to implement virtually untraceable scams. One of the typical scams that operate on Bitcoin are the so-called Ponzi schemes. These are fraudulent investments which repay users with the funds invested by new users that join the scheme, and implode when it is no longer possible to find new investments. Despite being illegal in many countries, Ponzi schemes are now proliferating on Bitcoin, and they keep alluring new victims, who are plundered of millions of dollars. We apply data mining techniques to detect Bitcoin addresses related to Ponzi schemes. Our starting point is a dataset of features of real-world Ponzi schemes, that we construct by analysing, on the Bitcoin blockchain, the transactions used to perform the scams. We use this dataset to experiment with various machine learning algorithms, and we assess their effectiveness through standard validation protocols and performance metrics. The best of the classifiers we have experimented can identify most of the Ponzi schemes in the dataset, with a low number of false positives