The general rule about arranging before Shabbat for a non-Jew to do work for you on Shabbat is as follows. If the non-Jew is considered to be acting independently for his own benefit, it is permitted, even though the Jew gains from the action. If halacha views him as serving as some type of shaliach (agent) of the Jew, it is forbidden. Based on this rule, the classical poskim arrived at a variety of practical distinctions.
One may not pay a non-Jew to be his employee (po’el) on Shabbat. However he may give a non-Jew a job to do if he is paid for the specific job (kablan), not for his commitment to do work on the Jew’s behalf.[1] There are many details and distinctions in these halachot, such as how we treat extended work relationships and marit ayin issues that arise when it looks like he is the Jew’s daily employee. However, these are beyond this response’s scope. What is most pertinent to us is the rule that the Jew may not demand even of a kablan that he do the work on Shabbat.[2] Even if the Jew does not specify that he work on Shabbat, if, in order to accomplish the job as specified, the non-Jew must work on Shabbat, the prohibition still applies.[3] This seems to apply in your case, as paying him for the task of buying the tickets requires that he do so on Shabbat.
However, the non-Jew is considered working for you only if the work relates to you directly. Therefore, although you may not give money to a non-Jew to purchase a commodity for you on Shabbat, you may suggest that he buy it with his own money and hint that you will likely buy it from him after Shabbat.[4] Hagahot Maimoniot[5] and Hagahot Mordechai[6] derive this from the fact that one can sell chametz to a non-Jew with the understanding that he will buy it back.[7] Since several Acharonim allow a Jew to give an oral assurance to buy back the chametz if the sale is unconditional,[8] one can likewise promise the non-Jew to buy the tickets from him after Shabbat.[9] There are those who even allow the Jew to lend the non-Jew money to buy the chametz because, at the time of the purchase, the money belongs to the non-Jew.[10]
In summary, you may suggest a deal; just don’t tell him to buy them for you.