Finance Applications of Game Theory

Traditional finance theory based on the assumptions of symmetric information and perfect and competitive markets has provided many important insights. These include the Modigliani and Miller Theorems, the CAPM, the Efficient Markets Hypothesis and continuous time finance. However, many empirical phenomena are difficult to reconcile with this traditional framework. Game theoretic techniques have allowed insights into a number of these. Many puzzles remain. This paper argues that recent advances in game theory concerned with higher order beliefs, informational cascades and heterogeneous prior beliefs have the potential to provide insights into some of these remaining puzzles.

Finance Applications of Game Theory

Traditional finance theory based on the assumptions of symmetric information and perfect and competitive markets has provided many important insights. These include the Modigliani and Miller Theorems, the CAPM, the Efficient Markets Hypothesis and continuous time finance. However, many empirical phenomena are difficult to reconcile with this traditional framework. Game theoretic techniques have allowed insights into a number of these. Many puzzles remain. This paper argues that recent advances in game theory concerned with higher order beliefs, informational cascades and heterogeneous prior beliefs have the potential to provide insights into some of these remaining puzzles.

Information acquisition and financial contagion.

This paper incorporates costly voluntary acquisition of information à la Nikitin and Smith (2007) [Nikitin, M., Smith, R.T., 2007. Information acquisition, coordination, and fundamentals in a financial crisis. Journal of Banking and Finance, in press, doi:10.1016/j.jbankfin.2007.04.031], in a framework similar to Allen and Gale (2000) [Allen, F., Gale, D., 2000. Financial contagion. Journal of Political Economy 108, 1–33], without relying on any unexpected shock to model contagion. In this framework, contagion and financial crises are the result of information gathering by depositors, weak fundamentals and an incomplete market structure of banks. It also shows how financial systems entering a recession can affect others with apparently stronger economic conditions (contagion). Finally, this is the first paper to investigate the effectiveness of the Contingent Credit Line procedures, introduced by the IMF at the end of the nineties, as a mechanism to prevent the propagation of crises.Central Bank; Contingent credit line; Financial contagion; Fundamentals; Verification equilibrium;

Beauty Contests, Bubbles and Iterated Expectations in Asset Markets

In a financial market where traders are risk averse and short lived, and prices are noisy, asset prices today depend on the average expectation today of tomorrow's price. Thus (iterating this relationship) the date 1 price equals the date 1 average expectation of the date 2 average expectation of the date 3 price. This will not in general equal the date 1 average expectation of the date 3 price. We show how this failure of the law of iterated expectations for average belief can help understand the role of higher order beliefs in a fully rational asset pricing model and explain over-reaction to (noisy) public information.Beauty Contests, Bubbles and iterated expectations in Asset Markets

Chromatic thresholds in dense random graphs

The chromatic threshold $\delta_\chi(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with minimum degree $\delta(G) \ge dpn$ has bounded chromatic number. The study of the parameter $\delta_\chi(H) := \delta_\chi(H,1)$ was initiated in 1973 by Erd\H{o}s and Simonovits, and was recently determined for all graphs $H$. In this paper we show that $\delta_\chi(H,p) = \delta_\chi(H)$ for all fixed $p \in (0,1)$, but that typically $\delta_\chi(H,p) \ne \delta_\chi(H)$ if $p = o(1)$. We also make significant progress towards determining $\delta_\chi(H,p)$ for all graphs $H$ in the range $p = n^{-o(1)}$. In sparser random graphs the problem is somewhat more complicated, and is studied in a separate paper.Comment: 36 pages (including appendix), 1 figure; the appendix is copied with minor modifications from arXiv:1108.1746 for a self-contained proof of a technical lemma; accepted to Random Structures and Algorithm

Prophetic theology in the Kairos tradition : a pentecostal and reformed perspective in black liberation theology in South Africa

This study focused on the ‘silence of the prophets’ in the post-apartheid era. It sought to understand why the prophets, who spoke out so vehemently against the injustices of apartheid, did not speak out against the injustices of the government after 1994 even when it became blatantly apparent that corruption was beginning to unfold on various levels, especially with the introduction of the so-called Arms Deal. Accordingly, the study singles out Drs Allan Boesak and Frank Chikane who were among the fiercest opponents of the apartheid regime before 1994. The study traced the impact of the ideological forces that influenced Boesak and Chikane’s ideological thinking from the early Slave Religion, Black Theology in the USA and Liberation Theology in Latin America. Black Theology and Black Consciousness first made their appearance in South Africa in the 1970s, with Boesak and Chikane, among others, as early advocates of these movements. In 1983, Boesak and Chikane took part in the launch of the United Democratic Front (UDF) in Mitchells Plain, Cape Town. This movement became the voice of the voiceless in an era when the members of the African National Congress (ANC) and Pan African Congress (PAC) had been sent into exile. It also signalled a more inclusive and reconciliatory shift in Boesak and Chikane’s Ideological thinking. Whereas Black Consciousness sought to exclude white people from participating in the struggle for liberation, the UDF united all under one banner without consideration for colour, race, religion or creed. After the advent of liberation in South Africa in 1994, it became increasingly obvious that corruption was infiltrating many levels of the new government. But the prophets were silent. Why were they silent? The study presents an analysis of the possible reasons for this silence based on interviews with Boesak and Chikane as role players and draws conclusions based on their writings both before and after 1994. Overall, the study concluded that they were silent because they had become part of the new political structures that had taken over power. To sum up, the study demonstrates the irony of prophetic oscillation and concludes that no prophet is a prophet for all times. Thus, as a new democracy unfolds in South Africa, the situation demands new prophets with a new message.Philosophy, Practical and Systematic TheologyD. Phil. (Theology