We are so used to Trump giving misleading or false statements. Granted, some of his claims he said simply because he just doesn’t know better. That’s a pity that someone in his position has, in fact, so little knowledge about matters that concern his country and the world. However, an abundance of these statements were given despite him knowing that they were wrong. Trump is well-known to outright lie in order to obtain personal advantages.

One recent claim making the news is that both Trump and his wife were tested Covid-19 positive. The first thought that comes to one’s mind is, of course, whether or not this is yet another one of his lies and fake news, or whether this is true. In fact, without him falling seriously ill, we will never know. So how can we assess whether this may be real or fake news, and what the press should report? Should reporters question his statement and call it fake, or should they present this to the world as the possible truth? Who will gain and who would lose?

This is a difficult question which is tough to answer without a deeper look at the potential gains and losses. Game Theory comes to our aid here. Let’s take a look at the potential trade offs, see the table below. An impartial reporter may either report the news as fake or as real. For Trump, there are four possibilities, three of which are choices: either he lies about being Covid-19 positive, or he says nothing (assuming he doesn’t have it). Another option is that he is actually Covid-19 positive. He could have also kept it quiet, so speaking the truth is an actual choice (if he falls sick while keeping quiet about it he could have claimed he didn’t know he had Covid-19, or that it spread really quickly). If he speaks the truth then there are two potential outcomes – one being that he will walk away without any serious effect from Covid-19, or he speaks the truth and will need to be hospitalized with severe impacts.

Reporters’ dominant strategy

In fact, for a reporter it does not really matter whether (s)he reports this as fake news or real news apart from in one case: if Trump really speaks the truth and falls severely sick, then if the reporter reports this as fake news this could provide a loss to the reporter. Firstly, the reporter reported wrongly, and secondly Trump can claim that all the reporters lie while he himself always speaks the truth, which will undermine the trust in reporters. In all other cases we will never be sure whether Trump speaks the truth or lies, so reporting this to be fake or real news will simply lead to more confirmation bias. Thus, whatever happens, a reporter’s dominant strategy is to report this as real news.

Trump’s dominant strategy

Let’s look at what Trump’s dominant strategy should be. If the reporter reports this as fake news or real news, Trump gains both if he lies and if he speaks the truth (without him falling sick), as in both cases he can claim that Covid-19 has little effect, something he argued for a long time and that will clearly help him for the election. Not saying anything is never the dominant strategy (which is maybe also the reason why Trump has an opinion about everything, even though he has no actual knowledge about it).

If reporters claim this is fake news and if he speaks the truth and falls sick, then he gains because he can claim that reporters were always spreading fake news about him and this should increase the trust of undecided voters in him. After all, if the reporters lied about something as severe as Covid-19, then Trump will gain because he spoke the truth that he has it. In contrast, if reporters present this as real news, then Trump does not gain from this any longer as he, firstly, falls sick and cannot easily continue his election campaign; and, secondly, he undermined his voters’ trust in him as he always presented Covid-19 as something that is of little impact. So only in the case where reporters claim this is real news and Trump falls sick will he actually not benefit from all this.

So what is Trump’s dominant strategy? For sure he gains if he lies. In the end he can walk away saying that Covid-19 has little effect as he always claimed. He will gain even more if reporters present this as real news. If reporters suggest this is the truth and he falls sick, then he loses as suggested above. So in this case everything comes down to probabilities. If it is true that he has Covid-19, then for his age group the risk of falling severely sick (and dying) is 5%. If he views this as a sufficiently low probability (so he actually believes what he says), then ex ante it is likely that he believes he will walk away from this and, no matter what the reporters report, this situation will be to his favor. Hence, Trump’s dominant strategy is to lie in case he does not have Covid-19, and it is also to claim he has Covid-19, especially if he believes his chances of falling sick are very low.

Some final remarks

In the end, it is always a dominant strategy for Trump to lie if he does not have Covid-19. And it is a dominant strategy for Trump to claim he has Covid-19 if he has it. Given our assessment above, no reporter should have a personal incentive to write that (s)he doubts Trump’s claim. If Trump lies about having Covid-19, then he will gain big time from this as he can claim all this Covid-19 issue is just not such a big problem. Of course, he will simply ignore all the deaths in the US but he will gain those voters who were not entirely sure about the whole situation and have little first-hand experience. If he really has Covid-19, then he is bound to gain from this, too, unless he falls severely ill, the probability of which is quite low.

Given he is a gambler, does this suggest that he may have wanted to be infected as he is bound to benefit from this? No, because he could have simply lied about it, gone into isolation, and benefit much more from this.

While we have been unable to identify whether or not Trump lied about having Covid-19 or not, we have shown that he benefits from lying, and he benefits from having Covid-19, unless he falls severly sick. In any case, reporters should present this as real news.

What is, of course, a real disgrace is that Trump managed to undermine our belief in the words of him as the president to such a degree that we question him even on a matter such as this and have to resort to an in-depths analysis of his incentives here.