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We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game-a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically equivalent to a common interest game. We present a unified framework applicable for both potential and zero-sum equivalent games by deriving a simple but useful characterization of these games. This allows us to re-derive known criteria for potential games, as well as obtain several new criteria. In particular, we prove (1) new integral tests for potential games and for zero-sum equivalent games, (2) a new derivative test for zero-sum equivalent games, and (3) a new representation characterization for zero-sum equivalent games.

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Recently, the Korean government is promoting the joint recruitment of public institutions, in which public institutions performing a similar task set a common date of written tests for entry-level employment. In this study, we analyze the effects of this policy on job seekers and institutions. Using a game-theoretic model with two institutions and a continuum of job seekers, we obtain the following results. First, when job seekers’ preferences for the two institutions are identical and one institution is much preferred to the other one, the less preferred institution and job seekers suffer from joint recruitment because job opportunities at the less preferred institution are not fully utilized under joint recruitment. On the other hand, when each institution is preferred by a half of job seekers, joint recruitment improves the overall utility of job seekers by increasing the likelihood that job seekers enter their preferred institutions. If joint recruitment lowers the overall difficulty of getting a job, it benefits job seekers with low ability more than those with high ability. Based on these results, we evaluate the policy of joint recruitment and discuss policy alternatives.

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This paper analyzes the recent realized volatility and jump of US Dollar/Euro and UK Pound/Euro returns using the high frequency five minute with the nonparametric estimation during years 2010-2018 including year 2016 of UK's national vote of Brexit.
The empirical results show that before Brexit vote in year 2016 the Bipower volatilities of US Dollar/Euro and UK Pound/Euro returns have the time dependence effects such as daily and monthly effects, but they do not have weekly effects. But, they have asymmetrical properties on real rate of returns. However, after Brexit vote in year 2016 Bipower volatilities of US Dollar/Euro and UK Pound/Euro returns have only daily effects, but they do not have weekly and monthly effects. Furthermore, they do not have asymmetrical properties on real rate of returns.
Before Brexit vote in year 2016, the Bipower jumps of US Dollar/Euro returns were not affected by the previous jumps and they do not have asymmetrical properties. Before Brexit vote in year 2016, Bipower jumps of UK Pound/Euro returns were not affected by the previous rates of returns, but after Brexit vote, jumps of UK Pound/Euro returns were affected by the previous rates of returns. Jumps of UK Pound/Euro returns do not have asymmetrical effects of previous rates of returns and jumps.

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Transition probability density function (TPDF) or log-TPDF of a diffusion is quite useful in many ways. For example, it can be employed not only to estimate a diffusion by the maximum likelihood estimation but also to simulate data from a diffusion or to price an asset when the underlying process follows a diffusion. However, unfortunately, the true TPDF of a diffusion is unknown with a few exceptions in general. Starting from Aït-Sahalia (2002)'s pioneering work on approximate but explicit TPDF of a univariate time-homogeneous diffusion to Choi (2019a)'s recent work on closed-form approximate TPDF of a multivariate time-inhomogeneous jump diffusion, several researchers have subsequently established the way to approximate the TPDFs or log-TPDFs of more general diffusion models. This article explains how people have resolved problems to generalize the method from Aït-Sahalia(2002)'s paper to Choi(2013, 2015)'s multivariate time-inhomogeneous diffusions. Due to space constraints, explanations of detailed theories or assumptions for their proof are reduced to the minimum and we show important results, with tacit facts not described in the original papers. In addition, we also introduce papers derived from and related to those key studies.