Likely neither. The game concept will not be protectable by copyright, only the particular expression of it as fixed in a tangible medium of expression, which you have not done I imagine. You might be able to patent a method of game play, but if it's just an idea that is likely insufficient to allow you to file a properly enabling patent application.
Trade secrecy is your protection, but no network will sign a secrecy agreement for a game show idea before they see it, and once they see it they no longer need the secret.
Trademark and servicemark are the real protection, as that is how people know the games to select them to watch. Price Is Right, Let's Make a Deal, Who Want's To Be A Millionaire, etc. - it's the name that is the key, but to get that you have to use it.
So, the appropriate way is to put it on the air, register the servicemark and trademark, register the copyright on your airshows, and then pitch the networks. What you need is an IP lawyer or Entertainment lawyer to work with you on this.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
In addition to my colleague's answer, if the game follows a story line, it may be worth exploring Copyright protection in that regard. If the game has any novel platform (e.g., software or hardware that performs a serious of operations associated with, for example, the game play), tools, designs, game pieces that go along with the game, those should be considered for some utility or design protection. Consult an Patent Attorney - you will be able to disclose your idea to him.
The prior answers given respond well to your specific question. I would just add that a nondisclosure agreement would be useful. A nondisclosure agreement is basically an agreement with the entity to whom you disclose your idea that states that entity will keep your idea secret and not use it without your permission. Nondisclosure agreements (also known as NDAs) are common, but whether you can get a recipient to sign an NDA often depends on industry practice, your experience and connections in the industry, and other factors.
Neither one. Our intellectual property laws do not protect mere ideas. Our laws protect the persons and companies who engage in the hard work necessary transform an idea into a useful invention, or a work of art, literature, film, music or in this case--broadcast TV. If you want to "pitch" an idea for a game show (or any other TV show), the only way to guaranty protection is to require that those to whom you "pitch" the idea enter into a non-disclosure agreement (NDA) with you. While NDA's are enforceable, you won't get any major network or television producer to enter into one of them with you unless you already have a significant track record of success in the business. The attitude of television executives is that you need them more than they need you---and they are undoubtedly right in 99.9 percent of situations.
If you are serious about developing a game show, then don't expect the networks to hand you a pot of gold for giving them an idea---they are flooded with these kinds of ideas, many of which are provided gratuitously by people who are not looking for any compensation whatsoever. Rather, you need engage in tangible actions to develop your game show----you need at least a pilot episode or "sizzle" before anyone will take you seriously. This means that you will need to find investors to finance the development and filming of a network quality pilot for your game show. Even if you don't have the resources for a full 30 minutes pilot, at the very least you will need was is called a "sizzle"---a short pilot that provides investors and potential broadcast and production partners a sufficient taste to permit them to make an investment decision.
Make no mistake about it---what we are talking here is (a) investment (corporate law), and (b) television production (intellectual property law). Your first step--if you are serious--is to retain legal counsel with expertise in these areas, and with contacts among television producers and network executives. You need your legal counsel to assist you in laying the legal foundation for your project in a manner that will protect you and your company as you attempt to market your pilot or sizzle. You also need this person to assist you in raising the money that you will need to move this forward---don't expert that a network is going to be your banker---that is not how the business works.
Note that in California, New York and some other states, courts have recently recognized that persons who "pitch" an idea to a television network or producer which later uses that idea are entitled to some degree of compensation on an implied contract/unjust enrichment theory. This is a very positive development for the protection of people who "pitch" their "sizzles" to networks. But if all you bring to the table is a general idea, these cases probably won't help you very much---these cases assume that the person who is "pitching" a show has an actual product to pitch (such as a pilot episode of a program or a sizzle), rather than a pie-in-the-sky idea. Further, these cases also are indicative of why you need intellectual property/business counsel to guide you through the process of developing your idea into something that is commercially viable. If you are serious about your "idea", then hire a legal counsel, raise money, and perform the hard work that is necessary before you will be rewarded with valuable intellectual property rights.