Colored minority games

We study the behavior of simple models for financial markets with widely spread frequency either in the trading activity of agents or in the occurrence of basic events. The generic picture of a phase transition between information efficient and inefficient markets still persists even when agents trade on widely spread time-scales. We derive analytically the dependence of the critical threshold on the distribution of time-scales. We also address the issue of market efficiency as a function of frequency. In an inefficient market we find that the size of arbitrage opportunities is inversely proportional to the frequency of the events on which they occur. Greatest asymmetries in market outcomes are concentrated on the most rare events. The practical limits of the applications of these ideas to real markets are discussed in a specific example.Comment: 15 pages, 3 figure

Lying and Certainty

In the philosophical literature on the definition of lying, the analysis is generally restricted to cases of flat-out belief. This chapter considers the complex phenomenon of lies involving partial beliefs – beliefs ranging from mere uncertainty to absolute certainty. The first section analyses lies uttered while holding a graded belief in the falsity of the assertion, and presents a revised insincerity condition, requiring that the liar believes the assertion to be more likely to be false than true. The second section analyses assertions that express graded beliefs, exploring how mitigation and reinforcement can alter the insincerity conditions for lying. The last section considers the case of lies that attack certainty (knowledge-lies), understood as attempt to alter the hearer's graded belief

Truth and assertion: rules vs aims

There is a fundamental disagreement about which norm regulates assertion. Proponents of factive accounts argue that only true propositions are assertable, whereas proponents of non-factive accounts insist that at least some false propositions are. Puzzlingly, both views are supported by equally plausible (but apparently incompatible) linguistic data. This paper delineates an alternative solution: to understand truth as the aim of assertion, and pair this view with a non-factive rule. The resulting account is able to explain all the relevant linguistic data, and finds independent support from general considerations about the differences between rules and aims

Trading behavior and excess volatility in toy markets

We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive reactivity of agents. These issues are dealt with in detail in the simple case without public information. We also derive, for the general case, the critical learning rate above which trading behavior leads to turbulent dynamics of the market.Comment: 14 pages, 4 figures, minor change

Criticality of mostly informative samples: A Bayesian model selection approach

We discuss a Bayesian model selection approach to high dimensional data in the deep under sampling regime. The data is based on a representation of the possible discrete states $s$, as defined by the observer, and it consists of $M$ observations of the state. This approach shows that, for a given sample size $M$, not all states observed in the sample can be distinguished. Rather, only a partition of the sampled states $s$ can be resolved. Such partition defines an {\em emergent} classification $q_s$ of the states that becomes finer and finer as the sample size increases, through a process of {\em symmetry breaking} between states. This allows us to distinguish between the $resolution$ of a given representation of the observer defined states $s$, which is given by the entropy of $s$, and its $relevance$ which is defined by the entropy of the partition $q_s$. Relevance has a non-monotonic dependence on resolution, for a given sample size. In addition, we characterise most relevant samples and we show that they exhibit power law frequency distributions, generally taken as signatures of "criticality". This suggests that "criticality" reflects the relevance of a given representation of the states of a complex system, and does not necessarily require a specific mechanism of self-organisation to a critical point.Comment: 31 pages, 7 figure