In his paper, Eugene Fama gives the definition of a "fair game" as given below. I disagree. AFAIK, a martingale has the following property: $E[X_{t+\tau} | X_t] = X_t$. What am I missing?

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Footnote 9 says:

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And again, in a previous statement:

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    $\begingroup$ What does Footnote 9 say? $\endgroup$ – noob2 Jul 15 '20 at 17:47
  • $\begingroup$ @noob2 Nothing that would justify the zero in my opinion. I've updated. $\endgroup$ – s5s Jul 15 '20 at 18:00
  • $\begingroup$ What does it mean for martingales to be "incorrect"? $\endgroup$ – Acccumulation Jul 16 '20 at 5:46

The way I understand it is:

In equation 2 $x_{j, t + 1}$ is defined as the change in of $p_j$ over the period $t$ to $t + 1$. The formula says that the expectation of the change is zero which is the same as saying that the expectation of the original variable at $t+1$ is equal to its current value.


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