  In this paper we develop a Markov Chain Monte Carlo code to study the dark
matter properties in interpreting the recent observations of cosmic ray
electron/positron excesses. We assume that the dark matter particles couple
dominantly to leptons and consider two cases separately with annihilating or
decaying into lepton pairs. The constraint on the central density profile from
diffuse $\gamma$-rays around the Galactic center is also included in the Markov
Chain Monte Carlo code self-consistently. In the numerical study, 7 parameters
are introduced. We fit two data sets independently and find that for the Data
set I (PAMELA+ATIC), dark matter with $m_{\chi}\approx0.7$ TeV for annihilation
(or 1.4 TeV for decay) and pure $e^+e^-$ channel is favored, while for the Data
set II (PAMELA+Fermi-LAT+H.E.S.S.) $m_{\chi}\approx 2$ TeV for annihilation (or
4 TeV for decay) and the combination of $\mu^+\mu^-$ and $\tau^+\tau^-$ final
states can best fit the data. The H.E.S.S. observation of the Galactic center
$\gamma$-rays puts a strong constraint on the central density profile of the
dark matter halo for the annihilation dark matter scenario. In this case the
NFW profile which is regarded as the typical predication from the cold dark
matter scenario, is excluded with a high significance ($>5\sigma$). For the
decaying dark matter scenario, the constraint is much weaker.
